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| Meta Title | tfp.distributions.Inflated | TensorFlow Probability |
| Meta Description | A mixture of a point-mass and another distribution. |
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| Boilerpipe Text | A mixture of a point-mass and another distribution.
Inherits From:
Mixture
,
AutoCompositeTensorDistribution
,
Distribution
,
AutoCompositeTensor
tfp
.
distributions
.
Inflated
(
distribution
,
inflated_loc_logits
=
None
,
inflated_loc_probs
=
None
,
inflated_loc
=
0.0
,
inflated_loc_atol
=
None
,
inflated_loc_rtol
=
None
,
validate_args
=
False
,
allow_nan_stats
=
True
,
name
=
'Inflated'
)
Under the hood, this is implemented as a mixture.Mixture, and so
supports all of the methods of that class.
### Examples:
zinb
=
Inflated
(
tfd
.
NegativeBinomial
(
5.0
,
probs
=
0.1
),
inflated_loc_prob
=
0.2
)
sample
=
zinb
.
sample
(
seed
=
jax
.
random
.
PRNGKey
(
0
))
If
distribution
is a
CompositeTensor
s, then the resulting
Inflated
instance is a
CompositeTensor
as well. Otherwise, a non-
CompositeTensor
_Inflated
instance is created instead. Distribution subclasses that inherit from
Inflated
will also inherit from
CompositeTensor
.
Args
distribution
The tfp.Distribution to combine with a point mass at x. This
code is intended to be used only with discrete distributions; when used
with continuous distributions sampling will work but log_probs will be a
sum of values with different units.
inflated_loc_logits
A scalar or tensor containing the excess log-odds for
the point mass at inflated_loc. Only one of
inflated_loc_probs
or
inflated_loc_logits
should be passed in.
inflated_loc_probs
A scalar or tensor containing the mixture weights for
the point mass at inflated_loc. Only one of
inflated_loc_probs
or
inflated_loc_logits
should be passed in.
inflated_loc
A scalar or tensor containing the locations of the point
mass component of the mixture.
inflated_loc_atol
Non-negative
Tensor
of same
dtype
as
inflated_loc
and broadcastable shape. The absolute tolerance for
comparing closeness to
inflated_loc
. Default is
0
.
inflated_loc_rtol
Non-negative
Tensor
of same
dtype
as
inflated_loc
and broadcastable shape. The relative tolerance for
comparing closeness to
inflated_loc
. Default is
0
.
validate_args
If true, inconsistent batch or event sizes raise a runtime
error.
allow_nan_stats
If false, any undefined statistics for any batch memeber
raise an exception.
name
An optional name for the distribution.
Attributes
allow_nan_stats
Python
bool
describing behavior when a stat is undefined.
Stats return +/- infinity when it makes sense. E.g., the variance of a
Cauchy distribution is infinity. However, sometimes the statistic is
undefined, e.g., if a distribution's pdf does not achieve a maximum within
the support of the distribution, the mode is undefined. If the mean is
undefined, then by definition the variance is undefined. E.g. the mean for
Student's T for df = 1 is undefined (no clear way to say it is either + or -
infinity), so the variance = E[(X - mean)**2] is also undefined.
batch_shape
Shape of a single sample from a single event index as a
TensorShape
.
May be partially defined or unknown.
The batch dimensions are indexes into independent, non-identical
parameterizations of this distribution.
cat
components
distribution
The distribution used for the non-inflated part.
dtype
The
DType
of
Tensor
s handled by this
Distribution
.
event_shape
Shape of a single sample from a single batch as a
TensorShape
.
May be partially defined or unknown.
experimental_is_sharded
experimental_shard_axis_names
The list or structure of lists of active shard axis names.
inflated_loc
The location to add probability mass to.
inflated_loc_logits
The log-odds for the point mass part of the distribution.
inflated_loc_probs
The mixture weight(s) for the point mass part of the distribution.
name
Name prepended to all ops created by this
Distribution
.
name_scope
Returns a
tf.name_scope
instance for this class.
non_trainable_variables
Sequence of non-trainable variables owned by this module and its submodules.
num_components
parameters
Dictionary of parameters used to instantiate this
Distribution
.
reparameterization_type
Describes how samples from the distribution are reparameterized.
Currently this is one of the static instances
tfd.FULLY_REPARAMETERIZED
or
tfd.NOT_REPARAMETERIZED
.
submodules
Sequence of all sub-modules.
Submodules are modules which are properties of this module, or found as
properties of modules which are properties of this module (and so on).
a
=
tf
.
Module
()
b
=
tf
.
Module
()
c
=
tf
.
Module
()
a
.
b
=
b
b
.
c
=
c
list
(
a
.
submodules
)
==
[
b
,
c
]
True
list
(
b
.
submodules
)
==
[
c
]
True
list
(
c
.
submodules
)
==
[]
True
trainable_variables
Sequence of trainable variables owned by this module and its submodules.
validate_args
Python
bool
indicating possibly expensive checks are enabled.
variables
Sequence of variables owned by this module and its submodules.
Methods
batch_shape_tensor
View source
batch_shape_tensor
(
name
=
'batch_shape_tensor'
)
Shape of a single sample from a single event index as a 1-D
Tensor
.
The batch dimensions are indexes into independent, non-identical
parameterizations of this distribution.
Args
name
name to give to the op
Returns
batch_shape
Tensor
.
cdf
View source
cdf
(
value
,
name
=
'cdf'
,
**
kwargs
)
Cumulative distribution function.
Given random variable
X
, the cumulative distribution function
cdf
is:
cdf(x) := P[X <= x]
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
cdf
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
copy
View source
copy
(
**
override_parameters_kwargs
)
Creates a deep copy of the distribution.
Args
**override_parameters_kwargs
String/value dictionary of initialization
arguments to override with new values.
Returns
distribution
A new instance of
type(self)
initialized from the union
of self.parameters and override_parameters_kwargs, i.e.,
dict(self.parameters, **override_parameters_kwargs)
.
covariance
View source
covariance
(
name
=
'covariance'
,
**
kwargs
)
Covariance.
Covariance is (possibly) defined only for non-scalar-event distributions.
For example, for a length-
k
, vector-valued distribution, it is calculated
as,
Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
where
Cov
is a (batch of)
k x k
matrix,
0 <= (i, j) < k
, and
E
denotes expectation.
Alternatively, for non-vector, multivariate distributions (e.g.,
matrix-valued, Wishart),
Covariance
shall return a (batch of) matrices
under some vectorization of the events, i.e.,
Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
where
Cov
is a (batch of)
k' x k'
matrices,
0 <= (i, j) < k' = reduce_prod(event_shape)
, and
Vec
is some function
mapping indices of this distribution's event dimensions to indices of a
length-
k'
vector.
Args
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
covariance
Floating-point
Tensor
with shape
[B1, ..., Bn, k', k']
where the first
n
dimensions are batch coordinates and
k' = reduce_prod(self.event_shape)
.
cross_entropy
View source
cross_entropy
(
other
,
name
=
'cross_entropy'
)
Computes the (Shannon) cross entropy.
Denote this distribution (
self
) by
P
and the
other
distribution by
Q
. Assuming
P, Q
are absolutely continuous with respect to
one another and permit densities
p(x) dr(x)
and
q(x) dr(x)
, (Shannon)
cross entropy is defined as:
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
where
F
denotes the support of the random variable
X ~ P
.
Args
other
tfp.distributions.Distribution
instance.
name
Python
str
prepended to names of ops created by this function.
Returns
cross_entropy
self.dtype
Tensor
with shape
[B1, ..., Bn]
representing
n
different calculations of (Shannon) cross entropy.
entropy
View source
entropy
(
name
=
'entropy'
,
**
kwargs
)
Shannon entropy in nats.
entropy_lower_bound
View source
entropy_lower_bound
(
name
=
'entropy_lower_bound'
)
A lower bound on the entropy of this mixture model.
The bound below is not always very tight, and its usefulness depends
on the mixture probabilities and the components in use.
A lower bound is useful for ELBO when the
Mixture
is the variational
distribution:
\(
\log p(x) >= ELBO = \int q(z) \log p(x, z) dz + H[q]
\)
where \( p \) is the prior distribution, \( q \) is the variational,
and \( H[q] \) is the entropy of \( q \). If there is a lower bound
\( G[q] \) such that \( H[q] \geq G[q] \) then it can be used in
place of \( H[q] \).
For a mixture of distributions \( q(Z) = \sum_i c_i q_i(Z) \) with
\( \sum_i c_i = 1 \), by the concavity of \( f(x) = -x \log x \), a
simple lower bound is:
\(
\begin{align}
H[q] & = - \int q(z) \log q(z) dz \\\
& = - \int (\sum_i c_i q_i(z)) \log(\sum_i c_i q_i(z)) dz \\\
& \geq - \sum_i c_i \int q_i(z) \log q_i(z) dz \\\
& = \sum_i c_i H[q_i]
\end{align}
\)
This is the term we calculate below for \( G[q] \).
Args
name
A name for this operation (optional).
Returns
A lower bound on the Mixture's entropy.
event_shape_tensor
View source
event_shape_tensor
(
name
=
'event_shape_tensor'
)
Shape of a single sample from a single batch as a 1-D int32
Tensor
.
Args
name
name to give to the op
Returns
event_shape
Tensor
.
experimental_default_event_space_bijector
View source
experimental_default_event_space_bijector
(
*
args
,
**
kwargs
)
Bijector mapping the reals (R**n) to the event space of the distribution.
Distributions with continuous support may implement
_default_event_space_bijector
which returns a subclass of
tfp.bijectors.Bijector
that maps R**n to the distribution's event space.
For example, the default bijector for the
Beta
distribution
is
tfp.bijectors.Sigmoid()
, which maps the real line to
[0, 1]
, the
support of the
Beta
distribution. The default bijector for the
CholeskyLKJ
distribution is
tfp.bijectors.CorrelationCholesky
, which
maps R^(k * (k-1) // 2) to the submanifold of k x k lower triangular
matrices with ones along the diagonal.
The purpose of
experimental_default_event_space_bijector
is
to enable gradient descent in an unconstrained space for Variational
Inference and Hamiltonian Monte Carlo methods. Some effort has been made to
choose bijectors such that the tails of the distribution in the
unconstrained space are between Gaussian and Exponential.
For distributions with discrete event space, or for which TFP currently
lacks a suitable bijector, this function returns
None
.
Args
*args
Passed to implementation
_default_event_space_bijector
.
**kwargs
Passed to implementation
_default_event_space_bijector
.
Returns
event_space_bijector
Bijector
instance or
None
.
experimental_fit
View source
@classmethod
experimental_fit
(
value
,
sample_ndims
=
1
,
validate_args
=
False
,
**
init_kwargs
)
Instantiates a distribution that maximizes the likelihood of
x
.
Args
value
a
Tensor
valid sample from this distribution family.
sample_ndims
Positive
int
Tensor number of leftmost dimensions of
value
that index i.i.d. samples.
Default value:
1
.
validate_args
Python
bool
, default
False
. When
True
, distribution
parameters are checked for validity despite possibly degrading runtime
performance. When
False
, invalid inputs may silently render incorrect
outputs.
Default value:
False
.
**init_kwargs
Additional keyword arguments passed through to
cls.__init__
. These take precedence in case of collision with the
fitted parameters; for example,
tfd.Normal.experimental_fit([1., 1.], scale=20.)
returns a Normal
distribution with
scale=20.
rather than the maximum likelihood
parameter
scale=0.
.
Returns
maximum_likelihood_instance
instance of
cls
with parameters that
maximize the likelihood of
value
.
experimental_local_measure
View source
experimental_local_measure
(
value
,
backward_compat
=
False
,
**
kwargs
)
Returns a log probability density together with a
TangentSpace
.
A
TangentSpace
allows us to calculate the correct push-forward
density when we apply a transformation to a
Distribution
on
a strict submanifold of R^n (typically via a
Bijector
in the
TransformedDistribution
subclass). The density correction uses
the basis of the tangent space.
Args
value
float
or
double
Tensor
.
backward_compat
bool
specifying whether to fall back to returning
FullSpace
as the tangent space, and representing R^n with the standard
basis.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
log_prob
a
Tensor
representing the log probability density, of shape
sample_shape(x) + self.batch_shape
with values of type
self.dtype
.
tangent_space
a
TangentSpace
object (by default
FullSpace
)
representing the tangent space to the manifold at
value
.
Raises
UnspecifiedTangentSpaceError if
backward_compat
is False and
the
_experimental_tangent_space
attribute has not been defined.
experimental_sample_and_log_prob
View source
experimental_sample_and_log_prob
(
sample_shape
=
(),
seed
=
None
,
name
=
'sample_and_log_prob'
,
**
kwargs
)
Samples from this distribution and returns the log density of the sample.
The default implementation simply calls
sample
and
log_prob
:
def
_sample_and_log_prob
(
self
,
sample_shape
,
seed
,
**
kwargs
):
x
=
self
.
sample
(
sample_shape
=
sample_shape
,
seed
=
seed
,
**
kwargs
)
return
x
,
self
.
log_prob
(
x
,
**
kwargs
)
However, some subclasses may provide more efficient and/or numerically
stable implementations.
Args
sample_shape
integer
Tensor
desired shape of samples to draw.
Default value:
()
.
seed
PRNG seed; see
tfp.random.sanitize_seed
for details.
Default value:
None
.
name
name to give to the op.
Default value:
'sample_and_log_prob'
.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
samples
a
Tensor
, or structure of
Tensor
s, with prepended dimensions
sample_shape
.
log_prob
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
is_scalar_batch
View source
is_scalar_batch
(
name
=
'is_scalar_batch'
)
Indicates that
batch_shape == []
.
Args
name
Python
str
prepended to names of ops created by this function.
Returns
is_scalar_batch
bool
scalar
Tensor
.
is_scalar_event
View source
is_scalar_event
(
name
=
'is_scalar_event'
)
Indicates that
event_shape == []
.
Args
name
Python
str
prepended to names of ops created by this function.
Returns
is_scalar_event
bool
scalar
Tensor
.
kl_divergence
View source
kl_divergence
(
other
,
name
=
'kl_divergence'
)
Computes the Kullback--Leibler divergence.
Denote this distribution (
self
) by
p
and the
other
distribution by
q
. Assuming
p, q
are absolutely continuous with respect to reference
measure
r
, the KL divergence is defined as:
KL[p, q] = E_p[log(p(X)/q(X))]
= -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
= H[p, q] - H[p]
where
F
denotes the support of the random variable
X ~ p
,
H[., .]
denotes (Shannon) cross entropy, and
H[.]
denotes (Shannon) entropy.
Args
other
tfp.distributions.Distribution
instance.
name
Python
str
prepended to names of ops created by this function.
Returns
kl_divergence
self.dtype
Tensor
with shape
[B1, ..., Bn]
representing
n
different calculations of the Kullback-Leibler
divergence.
log_cdf
View source
log_cdf
(
value
,
name
=
'log_cdf'
,
**
kwargs
)
Log cumulative distribution function.
Given random variable
X
, the cumulative distribution function
cdf
is:
log_cdf(x) := Log[ P[X <= x] ]
Often, a numerical approximation can be used for
log_cdf(x)
that yields
a more accurate answer than simply taking the logarithm of the
cdf
when
x << -1
.
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
logcdf
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
log_prob
View source
log_prob
(
value
,
name
=
'log_prob'
,
**
kwargs
)
Log probability density/mass function.
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
log_prob
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
log_survival_function
View source
log_survival_function
(
value
,
name
=
'log_survival_function'
,
**
kwargs
)
Log survival function.
Given random variable
X
, the survival function is defined:
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
Typically, different numerical approximations can be used for the log
survival function, which are more accurate than
1 - cdf(x)
when
x >> 1
.
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
Tensor
of shape
sample_shape(x) + self.batch_shape
with values of type
self.dtype
.
mean
View source
mean
(
name
=
'mean'
,
**
kwargs
)
Mean.
mode
View source
mode
(
name
=
'mode'
,
**
kwargs
)
Mode.
param_shapes
View source
@classmethod
param_shapes
(
sample_shape
,
name
=
'DistributionParamShapes'
)
Shapes of parameters given the desired shape of a call to
sample()
. (deprecated)
This is a class method that describes what key/value arguments are required
to instantiate the given
Distribution
so that a particular shape is
returned for that instance's call to
sample()
.
Subclasses should override class method
_param_shapes
.
Args
sample_shape
Tensor
or python list/tuple. Desired shape of a call to
sample()
.
name
name to prepend ops with.
Returns
dict
of parameter name to
Tensor
shapes.
param_static_shapes
View source
@classmethod
param_static_shapes
(
sample_shape
)
param_shapes with static (i.e.
TensorShape
) shapes. (deprecated)
This is a class method that describes what key/value arguments are required
to instantiate the given
Distribution
so that a particular shape is
returned for that instance's call to
sample()
. Assumes that the sample's
shape is known statically.
Subclasses should override class method
_param_shapes
to return
constant-valued tensors when constant values are fed.
Args
sample_shape
TensorShape
or python list/tuple. Desired shape of a call
to
sample()
.
Returns
dict
of parameter name to
TensorShape
.
Raises
ValueError
if
sample_shape
is a
TensorShape
and is not fully defined.
parameter_properties
View source
@classmethod
parameter_properties
(
dtype
=
tf
.
float32
,
num_classes
=
None
)
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution's
Tensor
-valued constructor arguments.
Distribution subclasses are not required to implement
_parameter_properties
, so this method may raise
NotImplementedError
.
Providing a
_parameter_properties
implementation enables several advanced
features, including:
Distribution batch slicing (
sliced_distribution = distribution[i:j]
).
Automatic inference of
_batch_shape
and
_batch_shape_tensor
, which must otherwise be computed explicitly.
Automatic instantiation of the distribution within TFP's internal
property tests.
Automatic construction of 'trainable' instances of the distribution
using appropriate bijectors to avoid violating parameter constraints.
This enables the distribution family to be used easily as a
surrogate posterior in variational inference.
In the future, parameter property annotations may enable additional
functionality; for example, returning Distribution instances from
tf.vectorized_map
.
Args
dtype
Optional float
dtype
to assume for continuous-valued parameters.
Some constraining bijectors require advance knowledge of the dtype
because certain constants (e.g.,
tfb.Softplus.low
) must be
instantiated with the same dtype as the values to be transformed.
num_classes
Optional
int
Tensor
number of classes to assume when
inferring the shape of parameters for categorical-like distributions.
Otherwise ignored.
Returns
parameter_properties
A
str ->
tfp.python.internal.parameter_properties.ParameterProperties
dict mapping constructor argument names to
ParameterProperties`
instances.
Raises
NotImplementedError
if the distribution class does not implement
_parameter_properties
.
prob
View source
prob
(
value
,
name
=
'prob'
,
**
kwargs
)
Probability density/mass function.
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
prob
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
quantile
View source
quantile
(
value
,
name
=
'quantile'
,
**
kwargs
)
Quantile function. Aka 'inverse cdf' or 'percent point function'.
Given random variable
X
and
p in [0, 1]
, the
quantile
is:
quantile(p) := x such that P[X <= x] == p
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
quantile
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with
values of type
self.dtype
.
sample
View source
sample
(
sample_shape
=
(),
seed
=
None
,
name
=
'sample'
,
**
kwargs
)
Generate samples of the specified shape.
Note that a call to
sample()
without arguments will generate a single
sample.
Args
sample_shape
0D or 1D
int32
Tensor
. Shape of the generated samples.
seed
PRNG seed; see
tfp.random.sanitize_seed
for details.
name
name to give to the op.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
samples
a
Tensor
with prepended dimensions
sample_shape
.
stddev
View source
stddev
(
name
=
'stddev'
,
**
kwargs
)
Standard deviation.
Standard deviation is defined as,
stddev = E[(X - E[X])**2]**0.5
where
X
is the random variable associated with this distribution,
E
denotes expectation, and
stddev.shape = batch_shape + event_shape
.
Args
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
stddev
Floating-point
Tensor
with shape identical to
batch_shape + event_shape
, i.e., the same shape as
self.mean()
.
survival_function
View source
survival_function
(
value
,
name
=
'survival_function'
,
**
kwargs
)
Survival function.
Given random variable
X
, the survival function is defined:
survival_function(x) = P[X > x]
= 1 - P[X <= x]
= 1 - cdf(x).
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
Tensor
of shape
sample_shape(x) + self.batch_shape
with values of type
self.dtype
.
unnormalized_log_prob
View source
unnormalized_log_prob
(
value
,
name
=
'unnormalized_log_prob'
,
**
kwargs
)
Potentially unnormalized log probability density/mass function.
This function is similar to
log_prob
, but does not require that the
return value be normalized. (Normalization here refers to the total
integral of probability being one, as it should be by definition for any
probability distribution.) This is useful, for example, for distributions
where the normalization constant is difficult or expensive to compute. By
default, this simply calls
log_prob
.
Args
value
float
or
double
Tensor
.
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
unnormalized_log_prob
a
Tensor
of shape
sample_shape(x) + self.batch_shape
with values of type
self.dtype
.
variance
View source
variance
(
name
=
'variance'
,
**
kwargs
)
Variance.
Variance is defined as,
Var = E[(X - E[X])**2]
where
X
is the random variable associated with this distribution,
E
denotes expectation, and
Var.shape = batch_shape + event_shape
.
Args
name
Python
str
prepended to names of ops created by this function.
**kwargs
Named arguments forwarded to subclass implementation.
Returns
variance
Floating-point
Tensor
with shape identical to
batch_shape + event_shape
, i.e., the same shape as
self.mean()
.
with_name_scope
@classmethod
with_name_scope
(
method
)
Decorator to automatically enter the module name scope.
class
MyModule
(
tf
.
Module
):
@tf
.
Module
.
with_name_scope
def
__call__
(
self
,
x
):
if
not
hasattr
(
self
,
'w'
):
self
.
w
=
tf
.
Variable
(
tf
.
random
.
normal
([
x
.
shape
[
1
],
3
]))
return
tf
.
matmul
(
x
,
self
.
w
)
Using the above module would produce
tf.Variable
s and
tf.Tensor
s whose
names included the module name:
mod
=
MyModule
()
mod
(
tf
.
ones
([
1
,
2
]))
<
tf
.
Tensor
:
shape
=
(
1
,
3
),
dtype
=
float32
,
numpy
=...
,
dtype
=
float32
)
>
mod
.
w
<
tf
.
Variable
'my_module/Variable:0'
shape
=
(
2
,
3
)
dtype
=
float32
,
numpy
=...
,
dtype
=
float32
)
>
Args
method
The method to wrap.
Returns
The original method wrapped such that it enters the module's name scope.
__getitem__
View source
__getitem__
(
slices
)
Slices the batch axes of this distribution, returning a new instance.
b
=
tfd
.
Bernoulli
(
logits
=
tf
.
zeros
([
3
,
5
,
7
,
9
]))
b
.
batch_shape
# => [3, 5, 7, 9]
b2
=
b
[:,
tf
.
newaxis
,
...
,
-
2
:,
1
::
2
]
b2
.
batch_shape
# => [3, 1, 5, 2, 4]
x
=
tf
.
random
.
normal
([
5
,
3
,
2
,
2
])
cov
=
tf
.
matmul
(
x
,
x
,
transpose_b
=
True
)
chol
=
tf
.
linalg
.
cholesky
(
cov
)
loc
=
tf
.
random
.
normal
([
4
,
1
,
3
,
1
])
mvn
=
tfd
.
MultivariateNormalTriL
(
loc
,
chol
)
mvn
.
batch_shape
# => [4, 5, 3]
mvn
.
event_shape
# => [2]
mvn2
=
mvn
[:,
3
:,
...
,
::
-
1
,
tf
.
newaxis
]
mvn2
.
batch_shape
# => [4, 2, 3, 1]
mvn2
.
event_shape
# => [2]
Args
slices
slices from the [] operator
Returns
dist
A new
tfd.Distribution
instance with sliced parameters.
__iter__
View source
__iter__
() |
| Markdown | [Skip to main content](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Inflated#main-content)
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- tfp.bijectors
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors)
- [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AbsoluteValue)
- [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Ascending)
- [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AutoCompositeTensorBijector)
- [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AutoregressiveNetwork)
- [BatchNormalization](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/BatchNormalization)
- [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Blockwise)
- [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Chain)
- [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CholeskyOuterProduct)
- [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CholeskyToInvCholesky)
- [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Composition)
- [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky)
- [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Cumsum)
- [DiscreteCosineTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/DiscreteCosineTransform)
- [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Exp)
- [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Expm1)
- [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FFJORD)
- [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FillScaleTriL)
- [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FillTriangular)
- [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/FrechetCDF)
- [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GeneralizedExtremeValueCDF)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GeneralizedPareto)
- [Glow](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Glow)
- [GlowDefaultExitNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GlowDefaultExitNetwork)
- [GlowDefaultNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GlowDefaultNetwork)
- [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GompertzCDF)
- [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/GumbelCDF)
- [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Householder)
- [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Identity)
- [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Inline)
- [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Invert)
- [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/IteratedSigmoidCentered)
- [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/JointMap)
- [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/KumaraswamyCDF)
- [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/LambertWTail)
- [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Log)
- [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Log1p)
- [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MaskedAutoregressiveFlow)
- [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MatrixInverseTriL)
- [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MatvecLU)
- [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/MoyalCDF)
- [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/NormalCDF)
- [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Pad)
- [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Permute)
- [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Power)
- [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/PowerTransform)
- [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RationalQuadraticSpline)
- [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RayleighCDF)
- [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/RealNVP)
- [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Reciprocal)
- [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Reshape)
- [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Restructure)
- [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Scale)
- [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecDiag)
- [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLU)
- [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLinearOperator)
- [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecLinearOperatorBlock)
- [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ScaleMatvecTriL)
- [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Shift)
- [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/ShiftedGompertzCDF)
- [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid)
- [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sinh)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SinhArcsinh)
- [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SoftClip)
- [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softfloor)
- [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/SoftmaxCentered)
- [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softplus)
- [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Softsign)
- [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Split)
- [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Square)
- [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Tanh)
- [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/TransformDiagonal)
- [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Transpose)
- [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/UnitVector)
- [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/WeibullCDF)
- [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/masked_autoregressive_default_template)
- [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/masked_dense)
- [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/pack_sequence_as)
- [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/real_nvp_default_template)
- [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/tree_flatten)
- tfp.debugging
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging)
- benchmarking
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking)
- [BenchmarkTfFunctionConfig](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/BenchmarkTfFunctionConfig)
- [benchmark\_tf\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/benchmark_tf_function)
- [default\_benchmark\_config](https://www.tensorflow.org/probability/api_docs/python/tfp/debugging/benchmarking/default_benchmark_config)
- tfp.distributions
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions)
- [AutoCompositeTensorDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Autoregressive)
- [BatchBroadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BatchBroadcast)
- [BatchReshape](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BatchReshape)
- [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Bates)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Bernoulli)
- [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Beta)
- [BetaBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BetaBinomial)
- [BetaQuotient](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/BetaQuotient)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Binomial)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Blockwise)
- [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Categorical)
- [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Cauchy)
- [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Chi)
- [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Chi2)
- [CholeskyLKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/CholeskyLKJ)
- [DeterminantalPointProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DeterminantalPointProcess)
- [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Deterministic)
- [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Dirichlet)
- [DirichletMultinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DirichletMultinomial)
- [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution)
- [DoublesidedMaxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/DoublesidedMaxwell)
- [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Empirical)
- [ExpGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpGamma)
- [ExpInverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpInverseGamma)
- [ExpRelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExpRelaxedOneHotCategorical)
- [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Exponential)
- [ExponentiallyModifiedGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ExponentiallyModifiedGaussian)
- [FiniteDiscrete](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/FiniteDiscrete)
- [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gamma)
- [GammaGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GammaGamma)
- [GaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GaussianProcess)
- [GaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GaussianProcessRegressionModel)
- [GeneralizedExtremeValue](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedExtremeValue)
- [GeneralizedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedNormal)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/GeneralizedPareto)
- [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Geometric)
- [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Gumbel)
- [HalfCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfCauchy)
- [HalfNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfNormal)
- [HalfStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HalfStudentT)
- [HiddenMarkovModel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/HiddenMarkovModel)
- [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Horseshoe)
- [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Independent)
- [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Inflated)
- [InverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/InverseGamma)
- [InverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/InverseGaussian)
- [JohnsonSU](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JohnsonSU)
- [JointDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution)
- [JointDistribution.Root](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistribution/Root)
- [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionCoroutine)
- [JointDistributionCoroutineAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionCoroutineAutoBatched)
- [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionNamed)
- [JointDistributionNamedAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionNamedAutoBatched)
- [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionSequential)
- [JointDistributionSequentialAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/JointDistributionSequentialAutoBatched)
- [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Kumaraswamy)
- [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LKJ)
- [LambertWDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LambertWDistribution)
- [LambertWNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LambertWNormal)
- [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Laplace)
- [LinearGaussianStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LinearGaussianStateSpaceModel)
- [LogLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogLogistic)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogNormal)
- [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Logistic)
- [LogitNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/LogitNormal)
- [MarkovChain](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MarkovChain)
- [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Masked)
- [MatrixNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MatrixNormalLinearOperator)
- [MatrixTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MatrixTLinearOperator)
- [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Mixture)
- [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MixtureSameFamily)
- [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Moyal)
- [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Multinomial)
- [MultivariateNormalDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiag)
- [MultivariateNormalDiagPlusLowRank](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiagPlusLowRank)
- [MultivariateNormalDiagPlusLowRankCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalDiagPlusLowRankCovariance)
- [MultivariateNormalFullCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalFullCovariance)
- [MultivariateNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalLinearOperator)
- [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateNormalTriL)
- [MultivariateStudentTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/MultivariateStudentTLinearOperator)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NegativeBinomial)
- [NoncentralChi2](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NoncentralChi2)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Normal)
- [NormalInverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/NormalInverseGaussian)
- [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/OneHotCategorical)
- [OrderedLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/OrderedLogistic)
- [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PERT)
- [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Pareto)
- [PixelCNN](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PixelCNN)
- [PlackettLuce](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PlackettLuce)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Poisson)
- [PoissonLogNormalQuadratureCompound](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PoissonLogNormalQuadratureCompound)
- [PowerSpherical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/PowerSpherical)
- [ProbitBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ProbitBernoulli)
- [QuantizedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/QuantizedDistribution)
- [RegisterKL](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RegisterKL)
- [RelaxedBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RelaxedBernoulli)
- [RelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/RelaxedOneHotCategorical)
- [ReparameterizationType](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ReparameterizationType)
- [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Sample)
- [SigmoidBeta](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SigmoidBeta)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SinhArcsinh)
- [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Skellam)
- [SphericalUniform](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/SphericalUniform)
- [StoppingRatioLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StoppingRatioLogistic)
- [StudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentT)
- [StudentTProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentTProcess)
- [StudentTProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/StudentTProcessRegressionModel)
- [TransformedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TransformedDistribution)
- [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Triangular)
- [TruncatedCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TruncatedCauchy)
- [TruncatedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TruncatedNormal)
- [TwoPieceNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TwoPieceNormal)
- [TwoPieceStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/TwoPieceStudentT)
- [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform)
- [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VariationalGaussianProcess)
- [VectorDeterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VectorDeterministic)
- [VonMises](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VonMises)
- [VonMisesFisher](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/VonMisesFisher)
- [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Weibull)
- [WishartLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/WishartLinearOperator)
- [WishartTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/WishartTriL)
- [ZeroInflatedNegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/ZeroInflatedNegativeBinomial)
- [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Zipf)
- [independent\_joint\_distribution\_from\_structure](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/independent_joint_distribution_from_structure)
- [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/kl_divergence)
- [mvn\_conjugate\_linear\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/mvn_conjugate_linear_update)
- [normal\_conjugates\_known\_scale\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/normal_conjugates_known_scale_posterior)
- [normal\_conjugates\_known\_scale\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/normal_conjugates_known_scale_predictive)
- [quadrature\_scheme\_lognormal\_gauss\_hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/quadrature_scheme_lognormal_gauss_hermite)
- [quadrature\_scheme\_lognormal\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/quadrature_scheme_lognormal_quantiles)
- tfp.experimental
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental)
- [AutoCompositeTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor)
- [as\_composite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/as_composite)
- [auto\_composite\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_composite_tensor)
- [register\_composite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/register_composite)
- auto\_batching
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching)
- [Context](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/Context)
- [NumpyBackend](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/NumpyBackend)
- [TensorFlowBackend](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/TensorFlowBackend)
- [TensorType](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/TensorType)
- [Type](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/Type)
- [truthy](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/truthy)
- allocation\_strategy
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/allocation_strategy)
- [optimize](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/allocation_strategy/optimize)
- dsl
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/dsl)
- [ProgramBuilder](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/dsl/ProgramBuilder)
- frontend
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend)
- gast\_util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util)
- [Module](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Module)
- [Name](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Name)
- [Str](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/Str)
- [is\_constant](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_constant)
- [is\_ellipsis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_ellipsis)
- [is\_literal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/frontend/gast_util/is_literal)
- instructions
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions)
- [Block](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Block)
- [BranchOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/BranchOp)
- [ControlFlowGraph](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/ControlFlowGraph)
- [Function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Function)
- [FunctionCallOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/FunctionCallOp)
- [GotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/GotoOp)
- [IndirectGotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/IndirectGotoOp)
- [PopOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PopOp)
- [PrimOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PrimOp)
- [Program](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/Program)
- [PushGotoOp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/PushGotoOp)
- [VariableAllocation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/VariableAllocation)
- [extract\_referenced\_variables](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/extract_referenced_variables)
- [halt\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/halt_op)
- [interpret](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/interpret)
- [push\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/instructions/push_op)
- liveness
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/liveness)
- [liveness\_analysis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/liveness/liveness_analysis)
- lowering
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/lowering)
- [lower\_function\_calls](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/lowering/lower_function_calls)
- numpy\_backend
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/numpy_backend)
- stack\_optimization
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stack_optimization)
- [fuse\_pop\_push](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stack_optimization/fuse_pop_push)
- stackless
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless)
- [ExecutionQueue](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/ExecutionQueue)
- [execute](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/execute)
- [is\_running](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/stackless/is_running)
- tf\_backend
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/tf_backend)
- type\_inference
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference)
- [infer\_types](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/infer_types)
- [infer\_types\_from\_signature](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/infer_types_from_signature)
- [is\_inferring](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/is_inferring)
- [signature](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/signature)
- [type\_of\_pattern](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/type_inference/type_of_pattern)
- virtual\_machine
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine)
- [execute](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine/execute)
- [is\_staging](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/virtual_machine/is_staging)
- xla
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/xla)
- [compile\_nested\_output](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/auto_batching/xla/compile_nested_output)
- bayesopt
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt)
- acquisition
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition)
- [AcquisitionFunction](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/AcquisitionFunction)
- [GaussianProcessExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessExpectedImprovement)
- [GaussianProcessMaxValueEntropySearch](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessMaxValueEntropySearch)
- [GaussianProcessProbabilityOfImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessProbabilityOfImprovement)
- [GaussianProcessUpperConfidenceBound](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/GaussianProcessUpperConfidenceBound)
- [MCMCReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/MCMCReducer)
- [ParallelExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelExpectedImprovement)
- [ParallelProbabilityOfImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelProbabilityOfImprovement)
- [ParallelUpperConfidenceBound](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/ParallelUpperConfidenceBound)
- [StudentTProcessExpectedImprovement](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/StudentTProcessExpectedImprovement)
- [WeightedPowerScalarization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bayesopt/acquisition/WeightedPowerScalarization)
- bijectors
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors)
- [HighwayFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/HighwayFlow)
- [ScalarFunctionWithInferredInverse](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/ScalarFunctionWithInferredInverse)
- [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/Sharded)
- [build\_trainable\_highway\_flow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/build_trainable_highway_flow)
- [forward\_log\_det\_jacobian\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/forward_log_det_jacobian_ratio)
- [inverse\_log\_det\_jacobian\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/inverse_log_det_jacobian_ratio)
- [make\_distribution\_bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/bijectors/make_distribution_bijector)
- distribute
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute)
- [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionCoroutine)
- [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionNamed)
- [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/JointDistributionSequential)
- [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/Sharded)
- [make\_pbroadcast\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_pbroadcast_function)
- [make\_psum\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_psum_function)
- [make\_sharded\_log\_prob\_parts](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distribute/make_sharded_log_prob_parts)
- distributions
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions)
- [ImportanceResample](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/ImportanceResample)
- [IncrementLogProb](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/IncrementLogProb)
- [JointDistributionPinned](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/JointDistributionPinned)
- [MultiTaskGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultiTaskGaussianProcess)
- [MultiTaskGaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultiTaskGaussianProcessRegressionModel)
- [MultivariateNormalPrecisionFactorLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/MultivariateNormalPrecisionFactorLinearOperator)
- [inflated\_factory](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/inflated_factory)
- [log\_prob\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/log_prob_ratio)
- marginal\_fns
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns)
- [make\_backoff\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_backoff_cholesky)
- [make\_cholesky\_like\_marginal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_cholesky_like_marginal_fn)
- [make\_eigh\_marginal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/make_eigh_marginal_fn)
- [retrying\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/retrying_cholesky)
- mvn\_linear\_operator
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/mvn_linear_operator)
- ps
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps)
- [abs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/abs)
- [add](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/add)
- [argmax](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argmax)
- [argmin](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argmin)
- [argsort](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/argsort)
- [broadcast\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/broadcast_shape)
- [broadcast\_to](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/broadcast_to)
- [case](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/case)
- [cast](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cast)
- [ceil](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ceil)
- [concat](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/concat)
- [cond](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cond)
- [constant](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/constant)
- [convert\_to\_shape\_tensor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/convert_to_shape_tensor)
- [cumprod](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cumprod)
- [cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/cumsum)
- [dimension\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dimension_size)
- [equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/equal)
- [expand\_dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/expand_dims)
- [expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/expm1)
- [eye](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/eye)
- [fill](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/fill)
- [floor](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/floor)
- [gather](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/gather)
- [greater](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/greater)
- [identity](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/identity)
- [invert\_permutation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/invert_permutation)
- [is\_finite](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_finite)
- [is\_inf](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_inf)
- [is\_nan](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_nan)
- [is\_numpy](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/is_numpy)
- [less](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/less)
- [linspace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/linspace)
- [log](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/log)
- [log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/log1p)
- [logical\_and](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_and)
- [logical\_not](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_not)
- [logical\_or](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/logical_or)
- [maximum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/maximum)
- [minimum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/minimum)
- [nextafter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/nextafter)
- [non\_negative\_axis](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/non_negative_axis)
- [not\_equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/not_equal)
- [one\_hot](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/one_hot)
- [ones](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ones)
- [ones\_like](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/ones_like)
- [pad](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/pad)
- [pow](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/pow)
- [range](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/range)
- [rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rank)
- [rank\_from\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rank_from_shape)
- [reduce\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_all)
- [reduce\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_any)
- [reduce\_max](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_max)
- [reduce\_min](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_min)
- [reduce\_prod](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_prod)
- [reduce\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reduce_sum)
- [repeat](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/repeat)
- [reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reshape)
- [reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/reverse)
- [round](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/round)
- [rsqrt](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/rsqrt)
- [setdiff1d](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/setdiff1d)
- [shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/shape)
- [shape\_slice](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/shape_slice)
- [size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/size)
- [size0](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/size0)
- [slice](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/slice)
- [smart\_where](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/smart_where)
- [sort](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/sort)
- [split](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/split)
- [sqrt](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/sqrt)
- [stack](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/stack)
- [tensor\_scatter\_nd\_add](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_add)
- [tensor\_scatter\_nd\_sub](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_sub)
- [tensor\_scatter\_nd\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensor_scatter_nd_update)
- [tile](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tile)
- [top\_k](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/top_k)
- [unique](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/unique)
- [unstack](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/unstack)
- [where](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/where)
- [zeros](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/zeros)
- [zeros\_like](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/zeros_like)
- dtype\_util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util)
- [as\_numpy\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/as_numpy_dtype)
- [assert\_same\_float\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/assert_same_float_dtype)
- [base\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/base_dtype)
- [base\_equal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/base_equal)
- [common\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/common_dtype)
- [eps](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/eps)
- [is\_bool](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_bool)
- [is\_complex](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_complex)
- [is\_floating](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_floating)
- [is\_integer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_integer)
- [is\_numpy\_compatible](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/is_numpy_compatible)
- [max](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/max)
- [min](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/min)
- [name](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/name)
- [real\_dtype](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/real_dtype)
- [size](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/dtype_util/size)
- tensorshape\_util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util)
- [as\_list](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/as_list)
- [assert\_has\_rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/assert_has_rank)
- [assert\_is\_compatible\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/assert_is_compatible_with)
- [concatenate](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/concatenate)
- [constant\_value\_as\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/constant_value_as_shape)
- [dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/dims)
- [is\_compatible\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/is_compatible_with)
- [is\_fully\_defined](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/is_fully_defined)
- [merge\_with](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/merge_with)
- [num\_elements](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/num_elements)
- [rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/rank)
- [set\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/set_shape)
- [with\_rank](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/with_rank)
- [with\_rank\_at\_least](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/ps/tensorshape_util/with_rank_at_least)
- tfp\_custom\_gradient
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient)
- [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/custom_gradient)
- [is\_valid\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/is_valid_gradient)
- [prevent\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/distributions/marginal_fns/tfp_custom_gradient/prevent_gradient)
- joint\_distribution\_layers
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers)
- [Affine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Affine)
- [AffineLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/AffineLayer)
- [Conv2D](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Conv2D)
- [Lambda](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Lambda)
- [Sequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/Sequential)
- [SequentialLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/SequentialLayer)
- [make\_conv2d\_layer\_class](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/make_conv2d_layer_class)
- [make\_lambda\_layer\_class](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/joint_distribution_layers/make_lambda_layer_class)
- linalg
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg)
- [LinearOperatorInterpolatedPSDKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorInterpolatedPSDKernel)
- [LinearOperatorPSDKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorPSDKernel)
- [LinearOperatorRowBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorRowBlock)
- [LinearOperatorUnitary](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/LinearOperatorUnitary)
- [no\_pivot\_ldl](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/no_pivot_ldl)
- [simple\_robustified\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/simple_robustified_cholesky)
- marginalize
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize)
- [MarginalizableJointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize/MarginalizableJointDistributionCoroutine)
- [logeinsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/marginalize/logeinsumexp)
- math
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math)
- [exp\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/exp_pade_4_4)
- [expm1\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/expm1_pade_4_4)
- [log1p\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/log1p_pade_4_4)
- [log\_pade\_4\_4](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/log_pade_4_4)
- [patch\_manual\_special\_functions](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/patch_manual_special_functions)
- [reduce\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/reduce_logsumexp)
- [softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/math/softplus)
- mcmc
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc)
- [CovarianceReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/CovarianceReducer)
- [DiagonalMassMatrixAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/DiagonalMassMatrixAdaptation)
- [EllipticalSliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/EllipticalSliceSampler)
- [ExpectationsReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ExpectationsReducer)
- [GradientBasedTrajectoryLengthAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/GradientBasedTrajectoryLengthAdaptation)
- [GradientBasedTrajectoryLengthAdaptationResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/GradientBasedTrajectoryLengthAdaptationResults)
- [KernelBuilder](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/KernelBuilder)
- [KernelOutputs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/KernelOutputs)
- [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/NoUTurnSampler)
- [PotentialScaleReductionReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PotentialScaleReductionReducer)
- [PreconditionedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PreconditionedHamiltonianMonteCarlo)
- [PreconditionedNoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/PreconditionedNoUTurnSampler)
- [ProgressBarReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ProgressBarReducer)
- [Reducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/Reducer)
- [SNAPERHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SNAPERHamiltonianMonteCarlo)
- [SNAPERHamiltonianMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SNAPERHamiltonianMonteCarloResults)
- [SampleDiscardingKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SampleDiscardingKernel)
- [SampleSNAPERHamiltonianMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SampleSNAPERHamiltonianMonteCarloResults)
- [SequentialMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SequentialMonteCarlo)
- [SequentialMonteCarloResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/SequentialMonteCarloResults)
- [Sharded](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/Sharded)
- [StateWithHistory](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/StateWithHistory)
- [ThinningKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ThinningKernel)
- [TracingReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/TracingReducer)
- [VarianceReducer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/VarianceReducer)
- [WeightedParticles](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WeightedParticles)
- [WithReductions](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WithReductions)
- [WithReductionsKernelResults](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/WithReductionsKernelResults)
- [augment\_prior\_with\_state\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_prior_with_state_history)
- [augment\_with\_observation\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_with_observation_history)
- [augment\_with\_state\_history](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/augment_with_state_history)
- [chees\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/chees_criterion)
- [chees\_rate\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/chees_rate_criterion)
- [default\_make\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/default_make_hmc_kernel_fn)
- [ess\_below\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/ess_below_threshold)
- [gen\_make\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/gen_make_hmc_kernel_fn)
- [gen\_make\_transform\_hmc\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/gen_make_transform_hmc_kernel_fn)
- [infer\_trajectories](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/infer_trajectories)
- [init\_near\_unconstrained\_zero](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/init_near_unconstrained_zero)
- [log\_ess\_from\_log\_weights](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/log_ess_from_log_weights)
- [make\_rwmh\_kernel\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/make_rwmh_kernel_fn)
- [make\_tqdm\_progress\_bar\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/make_tqdm_progress_bar_fn)
- [particle\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/particle_filter)
- [reconstruct\_trajectories](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/reconstruct_trajectories)
- [remc\_thermodynamic\_integrals](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/remc_thermodynamic_integrals)
- [resample\_deterministic\_minimum\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_deterministic_minimum_error)
- [resample\_independent](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_independent)
- [resample\_stratified](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_stratified)
- [resample\_systematic](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/resample_systematic)
- [retry\_init](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/retry_init)
- [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_chain)
- [sample\_chain\_with\_burnin](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_chain_with_burnin)
- [sample\_fold](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_fold)
- [sample\_sequential\_monte\_carlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_sequential_monte_carlo)
- [sample\_snaper\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/sample_snaper_hmc)
- [simple\_heuristic\_tuning](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/simple_heuristic_tuning)
- [snaper\_criterion](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/snaper_criterion)
- [step\_kernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/step_kernel)
- [windowed\_adaptive\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/windowed_adaptive_hmc)
- [windowed\_adaptive\_nuts](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/mcmc/windowed_adaptive_nuts)
- nn
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn)
- [Affine](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Affine)
- [AffineVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalFlipout)
- [AffineVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalReparameterization)
- [AffineVariationalReparameterizationLocal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/AffineVariationalReparameterizationLocal)
- [Convolution](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Convolution)
- [ConvolutionTranspose](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTranspose)
- [ConvolutionTransposeVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTransposeVariationalFlipout)
- [ConvolutionTransposeVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionTransposeVariationalReparameterization)
- [ConvolutionV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionV2)
- [ConvolutionVariationalFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalFlipout)
- [ConvolutionVariationalFlipoutV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalFlipoutV2)
- [ConvolutionVariationalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalReparameterization)
- [ConvolutionVariationalReparameterizationV2](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/ConvolutionVariationalReparameterizationV2)
- [Layer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Layer)
- [Sequential](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/Sequential)
- [VariationalLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/VariationalLayer)
- initializers
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers)
- [glorot\_normal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/glorot_normal)
- [glorot\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/glorot_uniform)
- [he\_normal](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/he_normal)
- [he\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/initializers/he_uniform)
- losses
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses)
- [compute\_extra\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/compute_extra_loss)
- [kl\_divergence\_exact](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/kl_divergence_exact)
- [kl\_divergence\_monte\_carlo](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/kl_divergence_monte_carlo)
- [negloglik](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/losses/negloglik)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util)
- [CallOnce](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/CallOnce)
- [RandomVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/RandomVariable)
- [batchify\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/batchify_op)
- [display\_imgs](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/display_imgs)
- [expand\_dims](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/expand_dims)
- [flatten\_rightmost](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/flatten_rightmost)
- [halflife\_decay](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/halflife_decay)
- [im2row](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/im2row)
- [im2row\_index](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/im2row_index)
- [make\_convolution\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_fn)
- [make\_convolution\_transpose\_fn\_with\_dilation](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_dilation)
- [make\_convolution\_transpose\_fn\_with\_subkernels](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_subkernels)
- [make\_convolution\_transpose\_fn\_with\_subkernels\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_convolution_transpose_fn_with_subkernels_matrix)
- [make\_fit\_op](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_fit_op)
- [make\_kernel\_bias](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias)
- [make\_kernel\_bias\_posterior\_mvn\_diag](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias_posterior_mvn_diag)
- [make\_kernel\_bias\_prior\_spike\_and\_slab](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/make_kernel_bias_prior_spike_and_slab)
- [prepare\_conv\_args](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/prepare_conv_args)
- [prepare\_tuple\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/prepare_tuple_argument)
- [tfcompile](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/tfcompile)
- [trace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/trace)
- [tune\_dataset](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/tune_dataset)
- [variables\_load](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_load)
- [variables\_save](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_save)
- [variables\_summary](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/nn/util/variables_summary)
- parallel\_filter
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter)
- [kalman\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter/kalman_filter)
- [sample\_walk](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/parallel_filter/sample_walk)
- psd\_kernels
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels)
- [AdditiveKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/AdditiveKernel)
- [ContinuousAndCategoricalValues](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/ContinuousAndCategoricalValues)
- [FeatureScaledWithCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/FeatureScaledWithCategorical)
- [FeatureScaledWithEmbeddedCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/FeatureScaledWithEmbeddedCategorical)
- [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/Independent)
- [MultiTaskKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/MultiTaskKernel)
- [Separable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/psd_kernels/Separable)
- sequential
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential)
- [EnsembleKalmanFilterState](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/EnsembleKalmanFilterState)
- [IteratedFilter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/IteratedFilter)
- [ensemble\_adjustment\_kalman\_filter\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_adjustment_kalman_filter_update)
- [ensemble\_kalman\_filter\_log\_marginal\_likelihood](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_log_marginal_likelihood)
- [ensemble\_kalman\_filter\_predict](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_predict)
- [ensemble\_kalman\_filter\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/ensemble_kalman_filter_update)
- [extended\_kalman\_filter](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/extended_kalman_filter)
- [geometric\_cooling\_schedule](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/geometric_cooling_schedule)
- [inflate\_by\_scaled\_identity\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sequential/inflate_by_scaled_identity_fn)
- stats
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats)
- [RunningCentralMoments](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningCentralMoments)
- [RunningCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningCovariance)
- [RunningMean](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningMean)
- [RunningPotentialScaleReduction](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningPotentialScaleReduction)
- [RunningVariance](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/stats/RunningVariance)
- sts\_gibbs
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs)
- [GibbsSamplerState](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/GibbsSamplerState)
- [build\_model\_for\_gibbs\_fitting](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/build_model_for_gibbs_fitting)
- [fit\_with\_gibbs\_sampling](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/fit_with_gibbs_sampling)
- [get\_seasonal\_latents\_shape](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/get_seasonal_latents_shape)
- [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/sts_gibbs/one_step_predictive)
- substrates
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/substrates)
- tangent\_spaces
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces)
- [AxisAlignedSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/AxisAlignedSpace)
- [ConstantDiagonalSymmetricMatrixSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ConstantDiagonalSymmetricMatrixSpace)
- [FullSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/FullSpace)
- [GeneralSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/GeneralSpace)
- [ProbabilitySimplexSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ProbabilitySimplexSpace)
- [SphericalSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/SphericalSpace)
- [SymmetricMatrixSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/SymmetricMatrixSpace)
- [TangentSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/TangentSpace)
- [UnspecifiedTangentSpaceError](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/UnspecifiedTangentSpaceError)
- [ZeroSpace](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/tangent_spaces/ZeroSpace)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util)
- [DeferredModule](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/DeferredModule)
- [JitPublicMethods](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/JitPublicMethods)
- [make\_trainable](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/make_trainable)
- [make\_trainable\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/util/make_trainable_stateless)
- vi
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi)
- [build\_affine\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior)
- [build\_affine\_surrogate\_posterior\_from\_base\_distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_from_base_distribution)
- [build\_affine\_surrogate\_posterior\_from\_base\_distribution\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_from_base_distribution_stateless)
- [build\_affine\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_affine_surrogate_posterior_stateless)
- [build\_asvi\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_asvi_surrogate_posterior)
- [build\_asvi\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_asvi_surrogate_posterior_stateless)
- [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_factored_surrogate_posterior)
- [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_factored_surrogate_posterior_stateless)
- [build\_split\_flow\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/build_split_flow_surrogate_posterior)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util)
- [build\_linear\_operator\_zeros](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_linear_operator_zeros)
- [build\_trainable\_linear\_operator\_block](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_block)
- [build\_trainable\_linear\_operator\_diag](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_diag)
- [build\_trainable\_linear\_operator\_full\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_full_matrix)
- [build\_trainable\_linear\_operator\_tril](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/vi/util/build_trainable_linear_operator_tril)
- tfp.glm
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/glm)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Bernoulli)
- [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/BernoulliNormalCDF)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Binomial)
- [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/CustomExponentialFamily)
- [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/ExponentialFamily)
- [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/GammaExp)
- [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/GammaSoftplus)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/LogNormal)
- [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/LogNormalSoftplus)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NegativeBinomial)
- [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NegativeBinomialSoftplus)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Normal)
- [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/NormalReciprocal)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/Poisson)
- [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/PoissonSoftplus)
- [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/compute_predicted_linear_response)
- [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/convergence_criteria_small_relative_norm_weights_change)
- [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit)
- [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_one_step)
- [fit\_sparse](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_sparse)
- [fit\_sparse\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/glm/fit_sparse_one_step)
- tfp.layers
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers)
- [AutoregressiveTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/AutoregressiveTransform)
- [BlockwiseInitializer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/BlockwiseInitializer)
- [CategoricalMixtureOfOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/CategoricalMixtureOfOneHotCategorical)
- [Convolution1DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution1DFlipout)
- [Convolution1DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution1DReparameterization)
- [Convolution2DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution2DFlipout)
- [Convolution2DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution2DReparameterization)
- [Convolution3DFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution3DFlipout)
- [Convolution3DReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/Convolution3DReparameterization)
- [DenseFlipout](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseFlipout)
- [DenseLocalReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseLocalReparameterization)
- [DenseReparameterization](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseReparameterization)
- [DenseVariational](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DenseVariational)
- [DistributionLambda](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/DistributionLambda)
- [IndependentBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentBernoulli)
- [IndependentLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentLogistic)
- [IndependentNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentNormal)
- [IndependentPoisson](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/IndependentPoisson)
- [KLDivergenceAddLoss](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/KLDivergenceAddLoss)
- [KLDivergenceRegularizer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/KLDivergenceRegularizer)
- [MixtureLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureLogistic)
- [MixtureNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureNormal)
- [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MixtureSameFamily)
- [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/MultivariateNormalTriL)
- [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/OneHotCategorical)
- [VariableLayer](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/VariableLayer)
- [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/VariationalGaussianProcess)
- [default\_loc\_scale\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_loc_scale_fn)
- [default\_mean\_field\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_mean_field_normal_fn)
- [default\_multivariate\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/default_multivariate_normal_fn)
- conv\_variational
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/conv_variational)
- dense\_variational
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational)
- dense\_variational\_v2
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2)
- kullback\_leibler
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2/kullback_leibler)
- [augment\_kl\_xent\_docs](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/dense_variational_v2/kullback_leibler/augment_kl_xent_docs)
- distribution\_layer
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/distribution_layer)
- initializers
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/initializers)
- masked\_autoregressive
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/masked_autoregressive)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util)
- [deserialize\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util/deserialize_function)
- [serialize\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/util/serialize_function)
- variable\_input
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/variable_input)
- weight\_norm
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/weight_norm)
- [WeightNorm](https://www.tensorflow.org/probability/api_docs/python/tfp/layers/weight_norm/WeightNorm)
- tfp.math
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math)
- [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/math/MinimizeTraceableQuantities)
- [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/math/atan_difference)
- [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_rectilinear_nd_grid)
- [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_regular_1d_grid)
- [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/batch_interp_regular_nd_grid)
- [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_iv_ratio)
- [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_ive)
- [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bessel_kve)
- [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/math/betainc)
- [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/betaincinv)
- [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/math/bracket_root)
- [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/math/cholesky_concat)
- [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/math/cholesky_update)
- [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/clip_by_value_preserve_gradient)
- [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/custom_gradient)
- [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/math/dawsn)
- [dense\_to\_sparse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/dense_to_sparse)
- [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/math/diag_jacobian)
- [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/erfcinv)
- [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/erfcx)
- [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/math/fill_triangular)
- [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/fill_triangular_inverse)
- [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/math/find_root_chandrupatla)
- [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/math/find_root_secant)
- [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/math/gram_schmidt)
- [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_logdet)
- [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_quadratic_form_solve)
- [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_quadratic_form_solvevec)
- [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_solve)
- [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hpsd_solvevec)
- [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/igammacinv)
- [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/math/igammainv)
- [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/math/interp_regular_1d_grid)
- [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lambertw)
- [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lambertw_winitzki_approx)
- [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lbeta)
- [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log1mexp)
- [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log1psquare)
- [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_add_exp)
- [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_bessel_ive)
- [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_bessel_kve)
- [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_combinations)
- [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_cosh)
- [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_cumsum_exp)
- [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_gamma_correction)
- [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_gamma_difference)
- [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/log_sub_exp)
- [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/math/logerfc)
- [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/math/logerfcx)
- [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/math/low_rank_cholesky)
- [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_matrix_inverse)
- [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_reconstruct)
- [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/lu_solve)
- [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/math/minimize)
- [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/math/minimize_stateless)
- [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/math/owens_t)
- [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/math/pivoted_cholesky)
- [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_kahan_sum)
- [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_log_harmonic_mean_exp)
- [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_logmeanexp)
- [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/math/reduce_weighted_logsumexp)
- [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/math/round_exponential_bump_function)
- [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/math/scan_associative)
- [secant\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/math/secant_root)
- [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/math/smootherstep)
- [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/math/soft_sorting_matrix)
- [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/math/soft_threshold)
- [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/math/softplus_inverse)
- [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sparse_or_dense_matmul)
- [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sparse_or_dense_matvecmul)
- [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/math/sqrt1pm1)
- [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/math/trapz)
- [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/math/value_and_gradient)
- hypergeometric
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hypergeometric)
- [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/math/hypergeometric/hyp2f1_small_argument)
- ode
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode)
- [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/BDF)
- [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/ChosenBySolver)
- [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Diagnostics)
- [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/DormandPrince)
- [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Results)
- [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/math/ode/Solver)
- psd\_kernels
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels)
- [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/AutoCompositeTensorPsdKernel)
- [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ChangePoint)
- [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Constant)
- [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExpSinSquared)
- [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExponentialCurve)
- [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/ExponentiatedQuadratic)
- [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/FeatureScaled)
- [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/FeatureTransformed)
- [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/GammaExponential)
- [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/GeneralizedMatern)
- [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/KumaraswamyTransformed)
- [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Linear)
- [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternFiveHalves)
- [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternOneHalf)
- [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/MaternThreeHalves)
- [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Parabolic)
- [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/PointwiseExponential)
- [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/Polynomial)
- [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/PositiveSemidefiniteKernel)
- [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/RationalQuadratic)
- [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/SchurComplement)
- [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/math/psd_kernels/SpectralMixture)
- tfp.mcmc
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc)
- [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/CheckpointableStatesAndTrace)
- [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/DualAveragingStepSizeAdaptation)
- [HamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/HamiltonianMonteCarlo)
- [MetropolisAdjustedLangevinAlgorithm](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/MetropolisAdjustedLangevinAlgorithm)
- [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/MetropolisHastings)
- [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/NoUTurnSampler)
- [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/RandomWalkMetropolis)
- [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/ReplicaExchangeMC)
- [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/SimpleStepSizeAdaptation)
- [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/SliceSampler)
- [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/StatesAndTrace)
- [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransformedTransitionKernel)
- [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransitionKernel)
- [UncalibratedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedHamiltonianMonteCarlo)
- [UncalibratedLangevin](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedLangevin)
- [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/UncalibratedRandomWalk)
- [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/default_swap_proposal_fn)
- [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/effective_sample_size)
- [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/even_odd_swap_proposal_fn)
- [make\_simple\_step\_size\_update\_policy](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/make_simple_step_size_update_policy)
- [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/potential_scale_reduction)
- [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/random_walk_normal_fn)
- [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/random_walk_uniform_fn)
- [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_annealed_importance_chain)
- [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_chain)
- [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/sample_halton_sequence)
- tfp.monte\_carlo
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/monte_carlo)
- [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/monte_carlo/expectation)
- tfp.optimizer
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer)
- [StochasticGradientLangevinDynamics](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/StochasticGradientLangevinDynamics)
- [VariationalSGD](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/VariationalSGD)
- [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/bfgs_minimize)
- [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/converged_all)
- [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/converged_any)
- [differential\_evolution\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/differential_evolution_minimize)
- [differential\_evolution\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/differential_evolution_one_step)
- [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/lbfgs_minimize)
- [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/nelder_mead_minimize)
- [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/nelder_mead_one_step)
- [proximal\_hessian\_sparse\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/proximal_hessian_sparse_minimize)
- [proximal\_hessian\_sparse\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/proximal_hessian_sparse_one_step)
- convergence\_criteria
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria)
- [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/ConvergenceCriterion)
- [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/LossNotDecreasing)
- [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated)
- linesearch
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/linesearch)
- [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/linesearch/hager_zhang)
- tfp.random
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/random)
- [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/random/rademacher)
- [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/random/rayleigh)
- [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed)
- [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/random/spherical_uniform)
- [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/random/split_seed)
- tfp.stats
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/stats)
- [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/assign_log_moving_mean_exp)
- [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/assign_moving_mean_variance)
- [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/auto_correlation)
- [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/brier_decomposition)
- [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/brier_score)
- [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/cholesky_covariance)
- [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/correlation)
- [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/count_integers)
- [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/covariance)
- [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/cumulative_variance)
- [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/expected_calibration_error)
- [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/expected_calibration_error_quantiles)
- [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/find_bins)
- [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/histogram)
- [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/kendalls_tau)
- [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_average_probs)
- [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_loomean_exp)
- [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_loosum_exp)
- [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_soomean_exp)
- [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/log_soosum_exp)
- [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/moving_mean_variance_zero_debiased)
- [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/percentile)
- [quantile\_auc](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/quantile_auc)
- [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/quantiles)
- [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/stddev)
- [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/variance)
- [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/windowed_mean)
- [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/stats/windowed_variance)
- tfp.sts
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/sts)
- [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AdditiveStateSpaceModel)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Autoregressive)
- [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveIntegratedMovingAverage)
- [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveMovingAverageStateSpaceModel)
- [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/AutoregressiveStateSpaceModel)
- [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/ConstrainedSeasonalStateSpaceModel)
- [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/DynamicLinearRegression)
- [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/DynamicLinearRegressionStateSpaceModel)
- [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/IntegratedStateSpaceModel)
- [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LinearRegression)
- [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLevel)
- [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLevelStateSpaceModel)
- [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLinearTrend)
- [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/LocalLinearTrendStateSpaceModel)
- [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MaskedTimeSeries)
- [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/MissingValuesTolerance)
- [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Seasonal)
- [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SeasonalStateSpaceModel)
- [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SemiLocalLinearTrend)
- [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SemiLocalLinearTrendStateSpaceModel)
- [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SmoothSeasonal)
- [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SmoothSeasonalStateSpaceModel)
- [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/SparseLinearRegression)
- [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/StructuralTimeSeries)
- [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/Sum)
- [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/build_factored_surrogate_posterior)
- [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/build_factored_surrogate_posterior_stateless)
- [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/decompose_by_component)
- [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/decompose_forecast_by_component)
- [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/fit_with_hmc)
- [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/forecast)
- [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/impute_missing_values)
- [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/moments_of_masked_time_series)
- [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/one_step_predictive)
- [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/regularize_series)
- [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/sts/sample_uniform_initial_state)
- tfp.substrates
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates)
- jax
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax)
- bijectors
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors)
- [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AbsoluteValue)
- [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Ascending)
- [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AutoCompositeTensorBijector)
- [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/AutoregressiveNetwork)
- [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Bijector)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Blockwise)
- [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Chain)
- [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CholeskyOuterProduct)
- [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CholeskyToInvCholesky)
- [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Composition)
- [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/CorrelationCholesky)
- [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Cumsum)
- [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Exp)
- [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Expm1)
- [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FFJORD)
- [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FillScaleTriL)
- [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FillTriangular)
- [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/FrechetCDF)
- [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GeneralizedExtremeValueCDF)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GeneralizedPareto)
- [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GompertzCDF)
- [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/GumbelCDF)
- [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Householder)
- [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Identity)
- [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Inline)
- [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Invert)
- [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/IteratedSigmoidCentered)
- [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/JointMap)
- [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/KumaraswamyCDF)
- [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/LambertWTail)
- [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Log)
- [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Log1p)
- [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MaskedAutoregressiveFlow)
- [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MatrixInverseTriL)
- [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MatvecLU)
- [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/MoyalCDF)
- [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/NormalCDF)
- [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Pad)
- [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Permute)
- [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Power)
- [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/PowerTransform)
- [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RationalQuadraticSpline)
- [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RayleighCDF)
- [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/RealNVP)
- [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Reciprocal)
- [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Reshape)
- [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Restructure)
- [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Scale)
- [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecDiag)
- [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLU)
- [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLinearOperator)
- [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecLinearOperatorBlock)
- [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ScaleMatvecTriL)
- [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Shift)
- [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/ShiftedGompertzCDF)
- [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Sigmoid)
- [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Sinh)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SinhArcsinh)
- [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SoftClip)
- [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softfloor)
- [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/SoftmaxCentered)
- [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softplus)
- [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Softsign)
- [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Split)
- [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Square)
- [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Tanh)
- [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/TransformDiagonal)
- [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/Transpose)
- [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/UnitVector)
- [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/WeibullCDF)
- [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/masked_autoregressive_default_template)
- [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/masked_dense)
- [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/pack_sequence_as)
- [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/real_nvp_default_template)
- [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/bijectors/tree_flatten)
- distributions
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions)
- [AutoCompositeTensorDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/AutoCompositeTensorDistribution)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Autoregressive)
- [BatchBroadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BatchBroadcast)
- [BatchReshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BatchReshape)
- [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Bates)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Bernoulli)
- [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Beta)
- [BetaBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BetaBinomial)
- [BetaQuotient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/BetaQuotient)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Binomial)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Blockwise)
- [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Categorical)
- [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Cauchy)
- [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Chi)
- [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Chi2)
- [CholeskyLKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/CholeskyLKJ)
- [DeterminantalPointProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DeterminantalPointProcess)
- [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Deterministic)
- [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Dirichlet)
- [DirichletMultinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DirichletMultinomial)
- [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Distribution)
- [DoublesidedMaxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/DoublesidedMaxwell)
- [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Empirical)
- [ExpGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpGamma)
- [ExpInverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpInverseGamma)
- [ExpRelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExpRelaxedOneHotCategorical)
- [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Exponential)
- [ExponentiallyModifiedGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ExponentiallyModifiedGaussian)
- [FiniteDiscrete](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/FiniteDiscrete)
- [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Gamma)
- [GammaGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GammaGamma)
- [GaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GaussianProcess)
- [GaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GaussianProcessRegressionModel)
- [GeneralizedExtremeValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedExtremeValue)
- [GeneralizedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedNormal)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/GeneralizedPareto)
- [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Geometric)
- [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Gumbel)
- [HalfCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfCauchy)
- [HalfNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfNormal)
- [HalfStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HalfStudentT)
- [HiddenMarkovModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/HiddenMarkovModel)
- [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Horseshoe)
- [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Independent)
- [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Inflated)
- [InverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/InverseGamma)
- [InverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/InverseGaussian)
- [JohnsonSU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JohnsonSU)
- [JointDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistribution)
- [JointDistribution.Root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistribution/Root)
- [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionCoroutine)
- [JointDistributionCoroutineAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionCoroutineAutoBatched)
- [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionNamed)
- [JointDistributionNamedAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionNamedAutoBatched)
- [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionSequential)
- [JointDistributionSequentialAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/JointDistributionSequentialAutoBatched)
- [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Kumaraswamy)
- [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LKJ)
- [LambertWDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LambertWDistribution)
- [LambertWNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LambertWNormal)
- [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Laplace)
- [LinearGaussianStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LinearGaussianStateSpaceModel)
- [LogLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogLogistic)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogNormal)
- [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Logistic)
- [LogitNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/LogitNormal)
- [MarkovChain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MarkovChain)
- [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Masked)
- [MatrixNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MatrixNormalLinearOperator)
- [MatrixTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MatrixTLinearOperator)
- [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Mixture)
- [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MixtureSameFamily)
- [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Moyal)
- [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Multinomial)
- [MultivariateNormalDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiag)
- [MultivariateNormalDiagPlusLowRank](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiagPlusLowRank)
- [MultivariateNormalDiagPlusLowRankCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalDiagPlusLowRankCovariance)
- [MultivariateNormalFullCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalFullCovariance)
- [MultivariateNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalLinearOperator)
- [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateNormalTriL)
- [MultivariateStudentTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/MultivariateStudentTLinearOperator)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NegativeBinomial)
- [NoncentralChi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NoncentralChi2)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Normal)
- [NormalInverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/NormalInverseGaussian)
- [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/OneHotCategorical)
- [OrderedLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/OrderedLogistic)
- [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PERT)
- [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Pareto)
- [PlackettLuce](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PlackettLuce)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Poisson)
- [PoissonLogNormalQuadratureCompound](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PoissonLogNormalQuadratureCompound)
- [PowerSpherical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/PowerSpherical)
- [ProbitBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ProbitBernoulli)
- [QuantizedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/QuantizedDistribution)
- [RegisterKL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RegisterKL)
- [RelaxedBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RelaxedBernoulli)
- [RelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/RelaxedOneHotCategorical)
- [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Sample)
- [SigmoidBeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SigmoidBeta)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SinhArcsinh)
- [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Skellam)
- [SphericalUniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/SphericalUniform)
- [StoppingRatioLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StoppingRatioLogistic)
- [StudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentT)
- [StudentTProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentTProcess)
- [StudentTProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/StudentTProcessRegressionModel)
- [TransformedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TransformedDistribution)
- [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Triangular)
- [TruncatedCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TruncatedCauchy)
- [TruncatedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TruncatedNormal)
- [TwoPieceNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TwoPieceNormal)
- [TwoPieceStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/TwoPieceStudentT)
- [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Uniform)
- [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VariationalGaussianProcess)
- [VectorDeterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VectorDeterministic)
- [VonMises](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VonMises)
- [VonMisesFisher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/VonMisesFisher)
- [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Weibull)
- [WishartLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/WishartLinearOperator)
- [WishartTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/WishartTriL)
- [ZeroInflatedNegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/ZeroInflatedNegativeBinomial)
- [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/Zipf)
- [independent\_joint\_distribution\_from\_structure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/independent_joint_distribution_from_structure)
- [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/kl_divergence)
- [mvn\_conjugate\_linear\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/mvn_conjugate_linear_update)
- [normal\_conjugates\_known\_scale\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/normal_conjugates_known_scale_posterior)
- [normal\_conjugates\_known\_scale\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/normal_conjugates_known_scale_predictive)
- [quadrature\_scheme\_lognormal\_gauss\_hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/quadrature_scheme_lognormal_gauss_hermite)
- [quadrature\_scheme\_lognormal\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/distributions/quadrature_scheme_lognormal_quantiles)
- glm
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Bernoulli)
- [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/BernoulliNormalCDF)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Binomial)
- [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/CustomExponentialFamily)
- [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/ExponentialFamily)
- [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/GammaExp)
- [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/GammaSoftplus)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/LogNormal)
- [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/LogNormalSoftplus)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NegativeBinomial)
- [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NegativeBinomialSoftplus)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Normal)
- [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/NormalReciprocal)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/Poisson)
- [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/PoissonSoftplus)
- [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/compute_predicted_linear_response)
- [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/convergence_criteria_small_relative_norm_weights_change)
- [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/fit)
- [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/glm/fit_one_step)
- math
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math)
- [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/MinimizeTraceableQuantities)
- [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/atan_difference)
- [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_rectilinear_nd_grid)
- [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_regular_1d_grid)
- [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/batch_interp_regular_nd_grid)
- [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_iv_ratio)
- [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_ive)
- [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bessel_kve)
- [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/betainc)
- [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/betaincinv)
- [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/bracket_root)
- [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/cholesky_concat)
- [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/cholesky_update)
- [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/clip_by_value_preserve_gradient)
- [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/custom_gradient)
- [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/dawsn)
- [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/diag_jacobian)
- [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/erfcinv)
- [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/erfcx)
- [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/fill_triangular)
- [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/fill_triangular_inverse)
- [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/find_root_chandrupatla)
- [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/find_root_secant)
- [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/gram_schmidt)
- [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_logdet)
- [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_quadratic_form_solve)
- [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_quadratic_form_solvevec)
- [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_solve)
- [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hpsd_solvevec)
- [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/igammacinv)
- [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/igammainv)
- [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/interp_regular_1d_grid)
- [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lambertw)
- [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lambertw_winitzki_approx)
- [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lbeta)
- [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log1mexp)
- [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log1psquare)
- [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_add_exp)
- [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_bessel_ive)
- [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_bessel_kve)
- [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_combinations)
- [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_cosh)
- [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_cumsum_exp)
- [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_gamma_correction)
- [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_gamma_difference)
- [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/log_sub_exp)
- [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/logerfc)
- [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/logerfcx)
- [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/low_rank_cholesky)
- [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_matrix_inverse)
- [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_reconstruct)
- [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/lu_solve)
- [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/minimize)
- [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/minimize_stateless)
- [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/owens_t)
- [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/pivoted_cholesky)
- [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_kahan_sum)
- [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_log_harmonic_mean_exp)
- [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_logmeanexp)
- [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/reduce_weighted_logsumexp)
- [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/round_exponential_bump_function)
- [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/scan_associative)
- [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/smootherstep)
- [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/soft_sorting_matrix)
- [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/soft_threshold)
- [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/softplus_inverse)
- [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sparse_or_dense_matmul)
- [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sparse_or_dense_matvecmul)
- [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/sqrt1pm1)
- [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/trapz)
- [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/value_and_gradient)
- hypergeometric
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hypergeometric)
- [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/hypergeometric/hyp2f1_small_argument)
- ode
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode)
- [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/BDF)
- [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/ChosenBySolver)
- [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Diagnostics)
- [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/DormandPrince)
- [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Results)
- [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/ode/Solver)
- psd\_kernels
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels)
- [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/AutoCompositeTensorPsdKernel)
- [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ChangePoint)
- [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Constant)
- [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExpSinSquared)
- [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExponentialCurve)
- [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/ExponentiatedQuadratic)
- [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/FeatureScaled)
- [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/FeatureTransformed)
- [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/GammaExponential)
- [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/GeneralizedMatern)
- [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/KumaraswamyTransformed)
- [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Linear)
- [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternFiveHalves)
- [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternOneHalf)
- [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/MaternThreeHalves)
- [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Parabolic)
- [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/PointwiseExponential)
- [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/Polynomial)
- [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/PositiveSemidefiniteKernel)
- [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/RationalQuadratic)
- [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/SchurComplement)
- [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/math/psd_kernels/SpectralMixture)
- mcmc
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc)
- [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/CheckpointableStatesAndTrace)
- [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/DualAveragingStepSizeAdaptation)
- [HamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/HamiltonianMonteCarlo)
- [MetropolisAdjustedLangevinAlgorithm](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/MetropolisAdjustedLangevinAlgorithm)
- [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/MetropolisHastings)
- [NoUTurnSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/NoUTurnSampler)
- [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/RandomWalkMetropolis)
- [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/ReplicaExchangeMC)
- [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/SimpleStepSizeAdaptation)
- [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/SliceSampler)
- [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/StatesAndTrace)
- [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/TransformedTransitionKernel)
- [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/TransitionKernel)
- [UncalibratedHamiltonianMonteCarlo](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedHamiltonianMonteCarlo)
- [UncalibratedLangevin](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedLangevin)
- [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/UncalibratedRandomWalk)
- [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/default_swap_proposal_fn)
- [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/effective_sample_size)
- [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/even_odd_swap_proposal_fn)
- [make\_simple\_step\_size\_update\_policy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/make_simple_step_size_update_policy)
- [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/potential_scale_reduction)
- [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/random_walk_normal_fn)
- [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/random_walk_uniform_fn)
- [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_annealed_importance_chain)
- [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_chain)
- [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/mcmc/sample_halton_sequence)
- monte\_carlo
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/monte_carlo)
- [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/monte_carlo/expectation)
- optimizer
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer)
- [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/bfgs_minimize)
- [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/converged_all)
- [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/converged_any)
- [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/lbfgs_minimize)
- [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/nelder_mead_minimize)
- [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/nelder_mead_one_step)
- convergence\_criteria
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria)
- [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/ConvergenceCriterion)
- [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/LossNotDecreasing)
- [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated)
- linesearch
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/linesearch)
- [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/optimizer/linesearch/hager_zhang)
- random
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random)
- [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/rademacher)
- [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/rayleigh)
- [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/sanitize_seed)
- [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/spherical_uniform)
- [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/random/split_seed)
- stats
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats)
- [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/assign_log_moving_mean_exp)
- [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/assign_moving_mean_variance)
- [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/auto_correlation)
- [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/brier_decomposition)
- [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/brier_score)
- [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/cholesky_covariance)
- [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/correlation)
- [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/count_integers)
- [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/covariance)
- [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/cumulative_variance)
- [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/expected_calibration_error)
- [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/expected_calibration_error_quantiles)
- [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/find_bins)
- [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/histogram)
- [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/kendalls_tau)
- [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_average_probs)
- [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_loomean_exp)
- [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_loosum_exp)
- [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_soomean_exp)
- [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/log_soosum_exp)
- [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/moving_mean_variance_zero_debiased)
- [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/percentile)
- [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/quantiles)
- [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/stddev)
- [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/variance)
- [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/windowed_mean)
- [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/stats/windowed_variance)
- sts
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts)
- [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AdditiveStateSpaceModel)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Autoregressive)
- [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveIntegratedMovingAverage)
- [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveMovingAverageStateSpaceModel)
- [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/AutoregressiveStateSpaceModel)
- [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/ConstrainedSeasonalStateSpaceModel)
- [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/DynamicLinearRegression)
- [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/DynamicLinearRegressionStateSpaceModel)
- [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/IntegratedStateSpaceModel)
- [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LinearRegression)
- [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLevel)
- [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLevelStateSpaceModel)
- [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLinearTrend)
- [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/LocalLinearTrendStateSpaceModel)
- [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/MaskedTimeSeries)
- [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/MissingValuesTolerance)
- [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Seasonal)
- [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SeasonalStateSpaceModel)
- [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SemiLocalLinearTrend)
- [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SemiLocalLinearTrendStateSpaceModel)
- [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SmoothSeasonal)
- [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SmoothSeasonalStateSpaceModel)
- [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/SparseLinearRegression)
- [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/StructuralTimeSeries)
- [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/Sum)
- [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/build_factored_surrogate_posterior)
- [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/build_factored_surrogate_posterior_stateless)
- [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/decompose_by_component)
- [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/decompose_forecast_by_component)
- [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/fit_with_hmc)
- [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/forecast)
- [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/impute_missing_values)
- [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/moments_of_masked_time_series)
- [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/one_step_predictive)
- [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/regularize_series)
- [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/sts/sample_uniform_initial_state)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util)
- [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/BatchedComponentProperties)
- [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/DeferredTensor)
- [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/ParameterProperties)
- [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/SeedStream)
- [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/util/TransformedVariable)
- vi
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi)
- [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/GradientEstimators)
- [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/amari_alpha)
- [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/arithmetic_geometric)
- [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/chi_square)
- [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/csiszar_vimco)
- [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/dual_csiszar_function)
- [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/fit_surrogate_posterior_stateless)
- [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/jeffreys)
- [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/jensen_shannon)
- [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/kl_forward)
- [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/kl_reverse)
- [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/log1p_abs)
- [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/modified_gan)
- [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/monte_carlo_variational_loss)
- [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/pearson)
- [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/squared_hellinger)
- [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/symmetrized_csiszar_function)
- [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/t_power)
- [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/total_variation)
- [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/jax/vi/triangular)
- numpy
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy)
- bijectors
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors)
- [AbsoluteValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AbsoluteValue)
- [Ascending](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Ascending)
- [AutoCompositeTensorBijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AutoCompositeTensorBijector)
- [AutoregressiveNetwork](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/AutoregressiveNetwork)
- [Bijector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Bijector)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Blockwise)
- [Chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Chain)
- [CholeskyOuterProduct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CholeskyOuterProduct)
- [CholeskyToInvCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CholeskyToInvCholesky)
- [Composition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Composition)
- [CorrelationCholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/CorrelationCholesky)
- [Cumsum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Cumsum)
- [Exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Exp)
- [Expm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Expm1)
- [FFJORD](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FFJORD)
- [FillScaleTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FillScaleTriL)
- [FillTriangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FillTriangular)
- [FrechetCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/FrechetCDF)
- [GeneralizedExtremeValueCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GeneralizedExtremeValueCDF)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GeneralizedPareto)
- [GompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GompertzCDF)
- [GumbelCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/GumbelCDF)
- [Householder](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Householder)
- [Identity](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Identity)
- [Inline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Inline)
- [Invert](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Invert)
- [IteratedSigmoidCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/IteratedSigmoidCentered)
- [JointMap](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/JointMap)
- [KumaraswamyCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/KumaraswamyCDF)
- [LambertWTail](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/LambertWTail)
- [Log](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Log)
- [Log1p](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Log1p)
- [MaskedAutoregressiveFlow](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MaskedAutoregressiveFlow)
- [MatrixInverseTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MatrixInverseTriL)
- [MatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MatvecLU)
- [MoyalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/MoyalCDF)
- [NormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/NormalCDF)
- [Pad](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Pad)
- [Permute](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Permute)
- [Power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Power)
- [PowerTransform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/PowerTransform)
- [RationalQuadraticSpline](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RationalQuadraticSpline)
- [RayleighCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RayleighCDF)
- [RealNVP](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/RealNVP)
- [Reciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Reciprocal)
- [Reshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Reshape)
- [Restructure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Restructure)
- [Scale](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Scale)
- [ScaleMatvecDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecDiag)
- [ScaleMatvecLU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLU)
- [ScaleMatvecLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLinearOperator)
- [ScaleMatvecLinearOperatorBlock](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecLinearOperatorBlock)
- [ScaleMatvecTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ScaleMatvecTriL)
- [Shift](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Shift)
- [ShiftedGompertzCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/ShiftedGompertzCDF)
- [Sigmoid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Sigmoid)
- [Sinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Sinh)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SinhArcsinh)
- [SoftClip](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SoftClip)
- [Softfloor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softfloor)
- [SoftmaxCentered](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/SoftmaxCentered)
- [Softplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softplus)
- [Softsign](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Softsign)
- [Split](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Split)
- [Square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Square)
- [Tanh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Tanh)
- [TransformDiagonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/TransformDiagonal)
- [Transpose](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/Transpose)
- [UnitVector](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/UnitVector)
- [WeibullCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/WeibullCDF)
- [masked\_autoregressive\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/masked_autoregressive_default_template)
- [masked\_dense](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/masked_dense)
- [pack\_sequence\_as](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/pack_sequence_as)
- [real\_nvp\_default\_template](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/real_nvp_default_template)
- [tree\_flatten](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/bijectors/tree_flatten)
- distributions
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions)
- [AutoCompositeTensorDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/AutoCompositeTensorDistribution)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Autoregressive)
- [BatchBroadcast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BatchBroadcast)
- [BatchReshape](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BatchReshape)
- [Bates](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Bates)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Bernoulli)
- [Beta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Beta)
- [BetaBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BetaBinomial)
- [BetaQuotient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/BetaQuotient)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Binomial)
- [Blockwise](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Blockwise)
- [Categorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Categorical)
- [Cauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Cauchy)
- [Chi](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Chi)
- [Chi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Chi2)
- [CholeskyLKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/CholeskyLKJ)
- [DeterminantalPointProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DeterminantalPointProcess)
- [Deterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Deterministic)
- [Dirichlet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Dirichlet)
- [DirichletMultinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DirichletMultinomial)
- [Distribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Distribution)
- [DoublesidedMaxwell](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/DoublesidedMaxwell)
- [Empirical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Empirical)
- [ExpGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpGamma)
- [ExpInverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpInverseGamma)
- [ExpRelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExpRelaxedOneHotCategorical)
- [Exponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Exponential)
- [ExponentiallyModifiedGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ExponentiallyModifiedGaussian)
- [FiniteDiscrete](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/FiniteDiscrete)
- [Gamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Gamma)
- [GammaGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GammaGamma)
- [GaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GaussianProcess)
- [GaussianProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GaussianProcessRegressionModel)
- [GeneralizedExtremeValue](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedExtremeValue)
- [GeneralizedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedNormal)
- [GeneralizedPareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/GeneralizedPareto)
- [Geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Geometric)
- [Gumbel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Gumbel)
- [HalfCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfCauchy)
- [HalfNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfNormal)
- [HalfStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HalfStudentT)
- [HiddenMarkovModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/HiddenMarkovModel)
- [Horseshoe](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Horseshoe)
- [Independent](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Independent)
- [Inflated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Inflated)
- [InverseGamma](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/InverseGamma)
- [InverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/InverseGaussian)
- [JohnsonSU](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JohnsonSU)
- [JointDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistribution)
- [JointDistribution.Root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistribution/Root)
- [JointDistributionCoroutine](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionCoroutine)
- [JointDistributionCoroutineAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionCoroutineAutoBatched)
- [JointDistributionNamed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionNamed)
- [JointDistributionNamedAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionNamedAutoBatched)
- [JointDistributionSequential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionSequential)
- [JointDistributionSequentialAutoBatched](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/JointDistributionSequentialAutoBatched)
- [Kumaraswamy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Kumaraswamy)
- [LKJ](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LKJ)
- [LambertWDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LambertWDistribution)
- [LambertWNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LambertWNormal)
- [Laplace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Laplace)
- [LinearGaussianStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LinearGaussianStateSpaceModel)
- [LogLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogLogistic)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogNormal)
- [Logistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Logistic)
- [LogitNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/LogitNormal)
- [MarkovChain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MarkovChain)
- [Masked](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Masked)
- [MatrixNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MatrixNormalLinearOperator)
- [MatrixTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MatrixTLinearOperator)
- [Mixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Mixture)
- [MixtureSameFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MixtureSameFamily)
- [Moyal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Moyal)
- [Multinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Multinomial)
- [MultivariateNormalDiag](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiag)
- [MultivariateNormalDiagPlusLowRank](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiagPlusLowRank)
- [MultivariateNormalDiagPlusLowRankCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalDiagPlusLowRankCovariance)
- [MultivariateNormalFullCovariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalFullCovariance)
- [MultivariateNormalLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalLinearOperator)
- [MultivariateNormalTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateNormalTriL)
- [MultivariateStudentTLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/MultivariateStudentTLinearOperator)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NegativeBinomial)
- [NoncentralChi2](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NoncentralChi2)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Normal)
- [NormalInverseGaussian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/NormalInverseGaussian)
- [OneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/OneHotCategorical)
- [OrderedLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/OrderedLogistic)
- [PERT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PERT)
- [Pareto](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Pareto)
- [PlackettLuce](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PlackettLuce)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Poisson)
- [PoissonLogNormalQuadratureCompound](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PoissonLogNormalQuadratureCompound)
- [PowerSpherical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/PowerSpherical)
- [ProbitBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ProbitBernoulli)
- [QuantizedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/QuantizedDistribution)
- [RegisterKL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RegisterKL)
- [RelaxedBernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RelaxedBernoulli)
- [RelaxedOneHotCategorical](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/RelaxedOneHotCategorical)
- [Sample](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Sample)
- [SigmoidBeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SigmoidBeta)
- [SinhArcsinh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SinhArcsinh)
- [Skellam](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Skellam)
- [SphericalUniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/SphericalUniform)
- [StoppingRatioLogistic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StoppingRatioLogistic)
- [StudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentT)
- [StudentTProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentTProcess)
- [StudentTProcessRegressionModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/StudentTProcessRegressionModel)
- [TransformedDistribution](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TransformedDistribution)
- [Triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Triangular)
- [TruncatedCauchy](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TruncatedCauchy)
- [TruncatedNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TruncatedNormal)
- [TwoPieceNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TwoPieceNormal)
- [TwoPieceStudentT](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/TwoPieceStudentT)
- [Uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Uniform)
- [VariationalGaussianProcess](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VariationalGaussianProcess)
- [VectorDeterministic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VectorDeterministic)
- [VonMises](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VonMises)
- [VonMisesFisher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/VonMisesFisher)
- [Weibull](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Weibull)
- [WishartLinearOperator](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/WishartLinearOperator)
- [WishartTriL](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/WishartTriL)
- [ZeroInflatedNegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/ZeroInflatedNegativeBinomial)
- [Zipf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/Zipf)
- [independent\_joint\_distribution\_from\_structure](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/independent_joint_distribution_from_structure)
- [kl\_divergence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/kl_divergence)
- [mvn\_conjugate\_linear\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/mvn_conjugate_linear_update)
- [normal\_conjugates\_known\_scale\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/normal_conjugates_known_scale_posterior)
- [normal\_conjugates\_known\_scale\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/normal_conjugates_known_scale_predictive)
- [quadrature\_scheme\_lognormal\_gauss\_hermite](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/quadrature_scheme_lognormal_gauss_hermite)
- [quadrature\_scheme\_lognormal\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/distributions/quadrature_scheme_lognormal_quantiles)
- glm
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm)
- [Bernoulli](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Bernoulli)
- [BernoulliNormalCDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/BernoulliNormalCDF)
- [Binomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Binomial)
- [CustomExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/CustomExponentialFamily)
- [ExponentialFamily](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/ExponentialFamily)
- [GammaExp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/GammaExp)
- [GammaSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/GammaSoftplus)
- [LogNormal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/LogNormal)
- [LogNormalSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/LogNormalSoftplus)
- [NegativeBinomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NegativeBinomial)
- [NegativeBinomialSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NegativeBinomialSoftplus)
- [Normal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Normal)
- [NormalReciprocal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/NormalReciprocal)
- [Poisson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/Poisson)
- [PoissonSoftplus](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/PoissonSoftplus)
- [compute\_predicted\_linear\_response](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/compute_predicted_linear_response)
- [convergence\_criteria\_small\_relative\_norm\_weights\_change](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/convergence_criteria_small_relative_norm_weights_change)
- [fit](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/fit)
- [fit\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/glm/fit_one_step)
- math
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math)
- [MinimizeTraceableQuantities](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/MinimizeTraceableQuantities)
- [atan\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/atan_difference)
- [batch\_interp\_rectilinear\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_rectilinear_nd_grid)
- [batch\_interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_regular_1d_grid)
- [batch\_interp\_regular\_nd\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/batch_interp_regular_nd_grid)
- [bessel\_iv\_ratio](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_iv_ratio)
- [bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_ive)
- [bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bessel_kve)
- [betainc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/betainc)
- [betaincinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/betaincinv)
- [bracket\_root](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/bracket_root)
- [cholesky\_concat](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/cholesky_concat)
- [cholesky\_update](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/cholesky_update)
- [clip\_by\_value\_preserve\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/clip_by_value_preserve_gradient)
- [custom\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/custom_gradient)
- [dawsn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/dawsn)
- [diag\_jacobian](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/diag_jacobian)
- [erfcinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/erfcinv)
- [erfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/erfcx)
- [fill\_triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/fill_triangular)
- [fill\_triangular\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/fill_triangular_inverse)
- [find\_root\_chandrupatla](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/find_root_chandrupatla)
- [find\_root\_secant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/find_root_secant)
- [gram\_schmidt](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/gram_schmidt)
- [hpsd\_logdet](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_logdet)
- [hpsd\_quadratic\_form\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_quadratic_form_solve)
- [hpsd\_quadratic\_form\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_quadratic_form_solvevec)
- [hpsd\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_solve)
- [hpsd\_solvevec](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hpsd_solvevec)
- [igammacinv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/igammacinv)
- [igammainv](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/igammainv)
- [interp\_regular\_1d\_grid](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/interp_regular_1d_grid)
- [lambertw](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lambertw)
- [lambertw\_winitzki\_approx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lambertw_winitzki_approx)
- [lbeta](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lbeta)
- [log1mexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log1mexp)
- [log1psquare](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log1psquare)
- [log\_add\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_add_exp)
- [log\_bessel\_ive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_bessel_ive)
- [log\_bessel\_kve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_bessel_kve)
- [log\_combinations](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_combinations)
- [log\_cosh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_cosh)
- [log\_cumsum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_cumsum_exp)
- [log\_gamma\_correction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_gamma_correction)
- [log\_gamma\_difference](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_gamma_difference)
- [log\_sub\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/log_sub_exp)
- [logerfc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/logerfc)
- [logerfcx](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/logerfcx)
- [low\_rank\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/low_rank_cholesky)
- [lu\_matrix\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_matrix_inverse)
- [lu\_reconstruct](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_reconstruct)
- [lu\_solve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/lu_solve)
- [minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/minimize)
- [minimize\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/minimize_stateless)
- [owens\_t](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/owens_t)
- [pivoted\_cholesky](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/pivoted_cholesky)
- [reduce\_kahan\_sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_kahan_sum)
- [reduce\_log\_harmonic\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_log_harmonic_mean_exp)
- [reduce\_logmeanexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_logmeanexp)
- [reduce\_weighted\_logsumexp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/reduce_weighted_logsumexp)
- [round\_exponential\_bump\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/round_exponential_bump_function)
- [scan\_associative](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/scan_associative)
- [smootherstep](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/smootherstep)
- [soft\_sorting\_matrix](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/soft_sorting_matrix)
- [soft\_threshold](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/soft_threshold)
- [softplus\_inverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/softplus_inverse)
- [sparse\_or\_dense\_matmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sparse_or_dense_matmul)
- [sparse\_or\_dense\_matvecmul](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sparse_or_dense_matvecmul)
- [sqrt1pm1](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/sqrt1pm1)
- [trapz](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/trapz)
- [value\_and\_gradient](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/value_and_gradient)
- hypergeometric
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hypergeometric)
- [hyp2f1\_small\_argument](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/hypergeometric/hyp2f1_small_argument)
- ode
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode)
- [BDF](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/BDF)
- [ChosenBySolver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/ChosenBySolver)
- [Diagnostics](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Diagnostics)
- [DormandPrince](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/DormandPrince)
- [Results](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Results)
- [Solver](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/ode/Solver)
- psd\_kernels
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels)
- [AutoCompositeTensorPsdKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/AutoCompositeTensorPsdKernel)
- [ChangePoint](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ChangePoint)
- [Constant](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Constant)
- [ExpSinSquared](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExpSinSquared)
- [ExponentialCurve](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExponentialCurve)
- [ExponentiatedQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/ExponentiatedQuadratic)
- [FeatureScaled](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/FeatureScaled)
- [FeatureTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/FeatureTransformed)
- [GammaExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/GammaExponential)
- [GeneralizedMatern](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/GeneralizedMatern)
- [KumaraswamyTransformed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/KumaraswamyTransformed)
- [Linear](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Linear)
- [MaternFiveHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternFiveHalves)
- [MaternOneHalf](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternOneHalf)
- [MaternThreeHalves](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/MaternThreeHalves)
- [Parabolic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Parabolic)
- [PointwiseExponential](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/PointwiseExponential)
- [Polynomial](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/Polynomial)
- [PositiveSemidefiniteKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/PositiveSemidefiniteKernel)
- [RationalQuadratic](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/RationalQuadratic)
- [SchurComplement](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/SchurComplement)
- [SpectralMixture](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/math/psd_kernels/SpectralMixture)
- mcmc
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc)
- [CheckpointableStatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/CheckpointableStatesAndTrace)
- [DualAveragingStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/DualAveragingStepSizeAdaptation)
- [MetropolisHastings](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/MetropolisHastings)
- [RandomWalkMetropolis](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/RandomWalkMetropolis)
- [ReplicaExchangeMC](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/ReplicaExchangeMC)
- [SimpleStepSizeAdaptation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/SimpleStepSizeAdaptation)
- [SliceSampler](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/SliceSampler)
- [StatesAndTrace](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/StatesAndTrace)
- [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/TransformedTransitionKernel)
- [TransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/TransitionKernel)
- [UncalibratedRandomWalk](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/UncalibratedRandomWalk)
- [default\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/default_swap_proposal_fn)
- [effective\_sample\_size](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/effective_sample_size)
- [even\_odd\_swap\_proposal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/even_odd_swap_proposal_fn)
- [potential\_scale\_reduction](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/potential_scale_reduction)
- [random\_walk\_normal\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/random_walk_normal_fn)
- [random\_walk\_uniform\_fn](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/random_walk_uniform_fn)
- [sample\_annealed\_importance\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_annealed_importance_chain)
- [sample\_chain](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_chain)
- [sample\_halton\_sequence](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/mcmc/sample_halton_sequence)
- monte\_carlo
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/monte_carlo)
- [expectation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/monte_carlo/expectation)
- optimizer
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer)
- [bfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/bfgs_minimize)
- [converged\_all](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/converged_all)
- [converged\_any](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/converged_any)
- [lbfgs\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/lbfgs_minimize)
- [nelder\_mead\_minimize](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/nelder_mead_minimize)
- [nelder\_mead\_one\_step](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/nelder_mead_one_step)
- convergence\_criteria
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria)
- [ConvergenceCriterion](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/ConvergenceCriterion)
- [LossNotDecreasing](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/LossNotDecreasing)
- [SuccessiveGradientsAreUncorrelated](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/convergence_criteria/SuccessiveGradientsAreUncorrelated)
- linesearch
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/linesearch)
- [hager\_zhang](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/optimizer/linesearch/hager_zhang)
- random
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random)
- [rademacher](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/rademacher)
- [rayleigh](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/rayleigh)
- [sanitize\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/sanitize_seed)
- [spherical\_uniform](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/spherical_uniform)
- [split\_seed](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/random/split_seed)
- stats
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats)
- [assign\_log\_moving\_mean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/assign_log_moving_mean_exp)
- [assign\_moving\_mean\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/assign_moving_mean_variance)
- [auto\_correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/auto_correlation)
- [brier\_decomposition](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/brier_decomposition)
- [brier\_score](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/brier_score)
- [cholesky\_covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/cholesky_covariance)
- [correlation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/correlation)
- [count\_integers](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/count_integers)
- [covariance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/covariance)
- [cumulative\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/cumulative_variance)
- [expected\_calibration\_error](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/expected_calibration_error)
- [expected\_calibration\_error\_quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/expected_calibration_error_quantiles)
- [find\_bins](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/find_bins)
- [histogram](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/histogram)
- [kendalls\_tau](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/kendalls_tau)
- [log\_average\_probs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_average_probs)
- [log\_loomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_loomean_exp)
- [log\_loosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_loosum_exp)
- [log\_soomean\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_soomean_exp)
- [log\_soosum\_exp](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/log_soosum_exp)
- [moving\_mean\_variance\_zero\_debiased](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/moving_mean_variance_zero_debiased)
- [percentile](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/percentile)
- [quantile\_auc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/quantile_auc)
- [quantiles](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/quantiles)
- [stddev](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/stddev)
- [variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/variance)
- [windowed\_mean](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/windowed_mean)
- [windowed\_variance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/stats/windowed_variance)
- sts
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts)
- [AdditiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AdditiveStateSpaceModel)
- [Autoregressive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Autoregressive)
- [AutoregressiveIntegratedMovingAverage](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveIntegratedMovingAverage)
- [AutoregressiveMovingAverageStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveMovingAverageStateSpaceModel)
- [AutoregressiveStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/AutoregressiveStateSpaceModel)
- [ConstrainedSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/ConstrainedSeasonalStateSpaceModel)
- [DynamicLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/DynamicLinearRegression)
- [DynamicLinearRegressionStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/DynamicLinearRegressionStateSpaceModel)
- [IntegratedStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/IntegratedStateSpaceModel)
- [LinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LinearRegression)
- [LocalLevel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLevel)
- [LocalLevelStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLevelStateSpaceModel)
- [LocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLinearTrend)
- [LocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/LocalLinearTrendStateSpaceModel)
- [MaskedTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/MaskedTimeSeries)
- [MissingValuesTolerance](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/MissingValuesTolerance)
- [Seasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Seasonal)
- [SeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SeasonalStateSpaceModel)
- [SemiLocalLinearTrend](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SemiLocalLinearTrend)
- [SemiLocalLinearTrendStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SemiLocalLinearTrendStateSpaceModel)
- [SmoothSeasonal](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SmoothSeasonal)
- [SmoothSeasonalStateSpaceModel](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SmoothSeasonalStateSpaceModel)
- [SparseLinearRegression](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/SparseLinearRegression)
- [StructuralTimeSeries](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/StructuralTimeSeries)
- [Sum](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/Sum)
- [build\_factored\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/build_factored_surrogate_posterior)
- [build\_factored\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/build_factored_surrogate_posterior_stateless)
- [decompose\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/decompose_by_component)
- [decompose\_forecast\_by\_component](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/decompose_forecast_by_component)
- [fit\_with\_hmc](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/fit_with_hmc)
- [forecast](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/forecast)
- [impute\_missing\_values](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/impute_missing_values)
- [moments\_of\_masked\_time\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/moments_of_masked_time_series)
- [one\_step\_predictive](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/one_step_predictive)
- [regularize\_series](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/regularize_series)
- [sample\_uniform\_initial\_state](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/sts/sample_uniform_initial_state)
- util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util)
- [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/BatchedComponentProperties)
- [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/DeferredTensor)
- [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/ParameterProperties)
- [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/SeedStream)
- [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/util/TransformedVariable)
- vi
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi)
- [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/GradientEstimators)
- [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/amari_alpha)
- [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/arithmetic_geometric)
- [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/chi_square)
- [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/csiszar_vimco)
- [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/dual_csiszar_function)
- [fit\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/fit_surrogate_posterior)
- [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/fit_surrogate_posterior_stateless)
- [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/jeffreys)
- [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/jensen_shannon)
- [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/kl_forward)
- [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/kl_reverse)
- [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/log1p_abs)
- [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/modified_gan)
- [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/monte_carlo_variational_loss)
- [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/pearson)
- [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/squared_hellinger)
- [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/symmetrized_csiszar_function)
- [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/t_power)
- [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/total_variation)
- [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/substrates/numpy/vi/triangular)
- tfp.util
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/util)
- [BatchedComponentProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/util/BatchedComponentProperties)
- [DeferredTensor](https://www.tensorflow.org/probability/api_docs/python/tfp/util/DeferredTensor)
- [ParameterProperties](https://www.tensorflow.org/probability/api_docs/python/tfp/util/ParameterProperties)
- [SeedStream](https://www.tensorflow.org/probability/api_docs/python/tfp/util/SeedStream)
- [TransformedVariable](https://www.tensorflow.org/probability/api_docs/python/tfp/util/TransformedVariable)
- tfp.vi
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/vi)
- [GradientEstimators](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/GradientEstimators)
- [amari\_alpha](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/amari_alpha)
- [arithmetic\_geometric](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/arithmetic_geometric)
- [chi\_square](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/chi_square)
- [csiszar\_vimco](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/csiszar_vimco)
- [dual\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/dual_csiszar_function)
- [fit\_surrogate\_posterior](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/fit_surrogate_posterior)
- [fit\_surrogate\_posterior\_stateless](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/fit_surrogate_posterior_stateless)
- [jeffreys](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/jeffreys)
- [jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/jensen_shannon)
- [kl\_forward](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/kl_forward)
- [kl\_reverse](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/kl_reverse)
- [log1p\_abs](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/log1p_abs)
- [modified\_gan](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/modified_gan)
- [monte\_carlo\_variational\_loss](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/monte_carlo_variational_loss)
- [pearson](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/pearson)
- [squared\_hellinger](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/squared_hellinger)
- [symmetrized\_csiszar\_function](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/symmetrized_csiszar_function)
- [t\_power](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/t_power)
- [total\_variation](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/total_variation)
- [triangular](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/triangular)
- mutual\_information
- [Overview](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information)
- [lower\_bound\_barber\_agakov](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_barber_agakov)
- [lower\_bound\_info\_nce](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_info_nce)
- [lower\_bound\_jensen\_shannon](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_jensen_shannon)
- [lower\_bound\_nguyen\_wainwright\_jordan](https://www.tensorflow.org/probability/api_docs/python/tfp/vi/mutual_information/lower_bound_nguyen_wainwright_jordan)
- [Introduction](https://www.tensorflow.org/learn)
- [Tutorials](https://www.tensorflow.org/tutorials)
- [Guide](https://www.tensorflow.org/guide)
- [Learn ML](https://www.tensorflow.org/resources/learn-ml)
- [TensorFlow (v2.16.1)](https://www.tensorflow.org/api/stable)
- [Versions…](https://www.tensorflow.org/versions)
- [TensorFlow.js](https://js.tensorflow.org/api/latest/)
- [TensorFlow Lite](https://www.tensorflow.org/lite/api_docs)
- [TFX](https://www.tensorflow.org/tfx/api_docs)
- LIBRARIES
- [TensorFlow.js](https://www.tensorflow.org/js)
- [TensorFlow Lite](https://www.tensorflow.org/lite)
- [TFX](https://www.tensorflow.org/tfx)
- [All libraries](https://www.tensorflow.org/resources/libraries-extensions)
- RESOURCES
- [Models & datasets](https://www.tensorflow.org/resources/models-datasets)
- [Tools](https://www.tensorflow.org/resources/tools)
- [Responsible AI](https://www.tensorflow.org/responsible_ai)
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- [Resources](https://www.tensorflow.org/resources)
- [Probability](https://www.tensorflow.org/probability)
- [API](https://www.tensorflow.org/probability/api_docs/python/tfp)
# tfp.distributions.InflatedStay organized with collections Save and categorize content based on your preferences.
| |
|---|
| [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/inflated.py#L234-L247) |
A mixture of a point-mass and another distribution.
Inherits From: [`Mixture`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Mixture), [`AutoCompositeTensorDistribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution), [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution), [`AutoCompositeTensor`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor)
```
tfp.distributions.Inflated(
distribution,
inflated_loc_logits=None,
inflated_loc_probs=None,
inflated_loc=0.0,
inflated_loc_atol=None,
inflated_loc_rtol=None,
validate_args=False,
allow_nan_stats=True,
name='Inflated'
)
```
Under the hood, this is implemented as a mixture.Mixture, and so supports all of the methods of that class.
\### Examples:
```
zinb = Inflated(
tfd.NegativeBinomial(5.0, probs=0.1), inflated_loc_prob=0.2)
sample = zinb.sample(seed=jax.random.PRNGKey(0))
```
If `distribution` is a `CompositeTensor`s, then the resulting `Inflated` instance is a `CompositeTensor` as well. Otherwise, a non-`CompositeTensor` `_Inflated` instance is created instead. Distribution subclasses that inherit from `Inflated` will also inherit from `CompositeTensor`.
| Args | |
|---|---|
| `distribution` | The tfp.Distribution to combine with a point mass at x. This code is intended to be used only with discrete distributions; when used with continuous distributions sampling will work but log\_probs will be a sum of values with different units. |
| `inflated_loc_logits` | A scalar or tensor containing the excess log-odds for the point mass at inflated\_loc. Only one of `inflated_loc_probs` or `inflated_loc_logits` should be passed in. |
| `inflated_loc_probs` | A scalar or tensor containing the mixture weights for the point mass at inflated\_loc. Only one of `inflated_loc_probs` or `inflated_loc_logits` should be passed in. |
| `inflated_loc` | A scalar or tensor containing the locations of the point mass component of the mixture. |
| `inflated_loc_atol` | Non-negative `Tensor` of same `dtype` as `inflated_loc` and broadcastable shape. The absolute tolerance for comparing closeness to `inflated_loc`. Default is `0`. |
| `inflated_loc_rtol` | Non-negative `Tensor` of same `dtype` as `inflated_loc` and broadcastable shape. The relative tolerance for comparing closeness to `inflated_loc`. Default is `0`. |
| `validate_args` | If true, inconsistent batch or event sizes raise a runtime error. |
| `allow_nan_stats` | If false, any undefined statistics for any batch memeber raise an exception. |
| `name` | An optional name for the distribution. |
| Attributes | |
|---|---|
| `allow_nan_stats` | Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E\[(X - mean)\*\*2\] is also undefined. |
| `batch_shape` | Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. |
| `cat` | |
| `components` | |
| `distribution` | The distribution used for the non-inflated part. |
| `dtype` | The `DType` of `Tensor`s handled by this `Distribution`. |
| `event_shape` | Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown. |
| `experimental_is_sharded` | |
| `experimental_shard_axis_names` | The list or structure of lists of active shard axis names. |
| `inflated_loc` | The location to add probability mass to. |
| `inflated_loc_logits` | The log-odds for the point mass part of the distribution. |
| `inflated_loc_probs` | The mixture weight(s) for the point mass part of the distribution. |
| `name` | Name prepended to all ops created by this `Distribution`. |
| `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. |
| `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules. **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
| `num_components` | |
| `parameters` | Dictionary of parameters used to instantiate this `Distribution`. |
| `reparameterization_type` | Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`. |
| `submodules` | Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). |
| `trainable_variables` | Sequence of trainable variables owned by this module and its submodules. **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
| `validate_args` | Python `bool` indicating possibly expensive checks are enabled. |
| `variables` | Sequence of variables owned by this module and its submodules.**Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. |
## Methods
### `batch_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L992-L1030)
```
batch_shape_tensor(
name='batch_shape_tensor'
)
```
Shape of a single sample from a single event index as a 1-D `Tensor`.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
| Args | |
|---|---|
| `name` | name to give to the op |
| Returns | |
|---|---|
| `batch_shape` | `Tensor`. |
### `cdf`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1411-L1429)
```
cdf(
value, name='cdf', **kwargs
)
```
Cumulative distribution function.
Given random variable `X`, the cumulative distribution function `cdf` is:
```
cdf(x) := P[X <= x]
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `cdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `copy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L896-L924)
```
copy(
**override_parameters_kwargs
)
```
Creates a deep copy of the distribution.
**Note:** the copy distribution may continue to depend on the original initialization arguments.
| Args | |
|---|---|
| `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. |
| Returns | |
|---|---|
| `distribution` | A new instance of `type(self)` initialized from the union of self.parameters and override\_parameters\_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. |
### `covariance`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1648-L1686)
```
covariance(
name='covariance', **kwargs
)
```
Covariance.
Covariance is (possibly) defined only for non-scalar-event distributions.
For example, for a length-`k`, vector-valued distribution, it is calculated as,
```
Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
```
where `Cov` is a (batch of) `k x k` matrix, `0 <= (i, j) < k`, and `E` denotes expectation.
Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), `Covariance` shall return a (batch of) matrices under some vectorization of the events, i.e.,
```
Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
```
where `Cov` is a (batch of) `k' x k'` matrices, `0 <= (i, j) < k' = reduce_prod(event_shape)`, and `Vec` is some function mapping indices of this distribution's event dimensions to indices of a length-`k'` vector.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `covariance` | Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`. |
### `cross_entropy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1701-L1724)
```
cross_entropy(
other, name='cross_entropy'
)
```
Computes the (Shannon) cross entropy.
Denote this distribution (`self`) by `P` and the `other` distribution by `Q`. Assuming `P, Q` are absolutely continuous with respect to one another and permit densities `p(x) dr(x)` and `q(x) dr(x)`, (Shannon) cross entropy is defined as:
```
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
```
where `F` denotes the support of the random variable `X ~ P`.
| Args | |
|---|---|
| `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. |
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `cross_entropy` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy. |
### `entropy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1524-L1527)
```
entropy(
name='entropy', **kwargs
)
```
Shannon entropy in nats.
### `entropy_lower_bound`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/mixture.py#L344-L390)
```
entropy_lower_bound(
name='entropy_lower_bound'
)
```
A lower bound on the entropy of this mixture model.
The bound below is not always very tight, and its usefulness depends on the mixture probabilities and the components in use.
A lower bound is useful for ELBO when the `Mixture` is the variational distribution:
\\( \\log p(x) \>= ELBO = \\int q(z) \\log p(x, z) dz + H\[q\] \\)
where \\( p \\) is the prior distribution, \\( q \\) is the variational, and \\( H\[q\] \\) is the entropy of \\( q \\). If there is a lower bound \\( G\[q\] \\) such that \\( H\[q\] \\geq G\[q\] \\) then it can be used in place of \\( H\[q\] \\).
For a mixture of distributions \\( q(Z) = \\sum\_i c\_i q\_i(Z) \\) with \\( \\sum\_i c\_i = 1 \\), by the concavity of \\( f(x) = -x \\log x \\), a simple lower bound is:
\\( \\begin{align} H\[q\] & = - \\int q(z) \\log q(z) dz \\\\\\ & = - \\int (\\sum\_i c\_i q\_i(z)) \\log(\\sum\_i c\_i q\_i(z)) dz \\\\\\ & \\geq - \\sum\_i c\_i \\int q\_i(z) \\log q\_i(z) dz \\\\\\ & = \\sum\_i c\_i H\[q\_i\] \\end{align} \\)
This is the term we calculate below for \\( G\[q\] \\).
| Args | |
|---|---|
| `name` | A name for this operation (optional). |
| Returns |
|---|
| A lower bound on the Mixture's entropy. |
### `event_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1099-L1125)
```
event_shape_tensor(
name='event_shape_tensor'
)
```
Shape of a single sample from a single batch as a 1-D int32 `Tensor`.
| Args | |
|---|---|
| `name` | name to give to the op |
| Returns | |
|---|---|
| `event_shape` | `Tensor`. |
### `experimental_default_event_space_bijector`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1768-L1797)
```
experimental_default_event_space_bijector(
*args, **kwargs
)
```
Bijector mapping the reals (R\*\*n) to the event space of the distribution.
Distributions with continuous support may implement `_default_event_space_bijector` which returns a subclass of [`tfp.bijectors.Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) that maps R\*\*n to the distribution's event space. For example, the default bijector for the `Beta` distribution is [`tfp.bijectors.Sigmoid()`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid), which maps the real line to `[0, 1]`, the support of the `Beta` distribution. The default bijector for the `CholeskyLKJ` distribution is [`tfp.bijectors.CorrelationCholesky`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky), which maps R^(k \* (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal.
The purpose of `experimental_default_event_space_bijector` is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential.
For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns `None`.
| Args | |
|---|---|
| `*args` | Passed to implementation `_default_event_space_bijector`. |
| `**kwargs` | Passed to implementation `_default_event_space_bijector`. |
| Returns | |
|---|---|
| `event_space_bijector` | `Bijector` instance or `None`. |
### `experimental_fit`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1799-L1847)
```
@classmethod
```
Instantiates a distribution that maximizes the likelihood of `x`.
| Args | |
|---|---|
| `value` | a `Tensor` valid sample from this distribution family. |
| `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. |
| `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. |
| `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. |
| Returns | |
|---|---|
| `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. |
### `experimental_local_measure`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1872-L1914)
```
experimental_local_measure(
value, backward_compat=False, **kwargs
)
```
Returns a log probability density together with a `TangentSpace`.
A `TangentSpace` allows us to calculate the correct push-forward density when we apply a transformation to a `Distribution` on a strict submanifold of R^n (typically via a `Bijector` in the `TransformedDistribution` subclass). The density correction uses the basis of the tangent space.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R^n with the standard basis. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
| `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. |
| Raises |
|---|
| UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. |
### `experimental_sample_and_log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1229-L1259)
```
experimental_sample_and_log_prob(
sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
)
```
Samples from this distribution and returns the log density of the sample.
The default implementation simply calls `sample` and `log_prob`:
```
def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
return x, self.log_prob(x, **kwargs)
```
However, some subclasses may provide more efficient and/or numerically stable implementations.
| Args | |
|---|---|
| `sample_shape` | integer `Tensor` desired shape of samples to draw. Default value: `()`. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. |
| `name` | name to give to the op. Default value: `'sample_and_log_prob'`. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. |
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `is_scalar_batch`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1156-L1168)
```
is_scalar_batch(
name='is_scalar_batch'
)
```
Indicates that `batch_shape == []`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `is_scalar_batch` | `bool` scalar `Tensor`. |
### `is_scalar_event`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1142-L1154)
```
is_scalar_event(
name='is_scalar_event'
)
```
Indicates that `event_shape == []`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `is_scalar_event` | `bool` scalar `Tensor`. |
### `kl_divergence`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1730-L1761)
```
kl_divergence(
other, name='kl_divergence'
)
```
Computes the Kullback--Leibler divergence.
Denote this distribution (`self`) by `p` and the `other` distribution by `q`. Assuming `p, q` are absolutely continuous with respect to reference measure `r`, the KL divergence is defined as:
```
KL[p, q] = E_p[log(p(X)/q(X))]
= -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
= H[p, q] - H[p]
```
where `F` denotes the support of the random variable `X ~ p`, `H[., .]` denotes (Shannon) cross entropy, and `H[.]` denotes (Shannon) entropy.
| Args | |
|---|---|
| `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. |
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `kl_divergence` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of the Kullback-Leibler divergence. |
### `log_cdf`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1373-L1395)
```
log_cdf(
value, name='log_cdf', **kwargs
)
```
Log cumulative distribution function.
Given random variable `X`, the cumulative distribution function `cdf` is:
```
log_cdf(x) := Log[ P[X <= x] ]
```
Often, a numerical approximation can be used for `log_cdf(x)` that yields a more accurate answer than simply taking the logarithm of the `cdf` when `x << -1`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `logcdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1275-L1287)
```
log_prob(
value, name='log_prob', **kwargs
)
```
Log probability density/mass function.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `log_survival_function`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1452-L1476)
```
log_survival_function(
value, name='log_survival_function', **kwargs
)
```
Log survival function.
Given random variable `X`, the survival function is defined:
```
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
```
Typically, different numerical approximations can be used for the log survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns |
|---|
| `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `mean`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1533-L1536)
```
mean(
name='mean', **kwargs
)
```
Mean.
### `mode`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1692-L1695)
```
mode(
name='mode', **kwargs
)
```
Mode.
### `param_shapes`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L701-L727)
```
@classmethod
```
Shapes of parameters given the desired shape of a call to `sample()`. (deprecated)
**Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.
This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`.
Subclasses should override class method `_param_shapes`.
| Args | |
|---|---|
| `sample_shape` | `Tensor` or python list/tuple. Desired shape of a call to `sample()`. |
| `name` | name to prepend ops with. |
| Returns |
|---|
| `dict` of parameter name to `Tensor` shapes. |
### `param_static_shapes`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L729-L769)
```
@classmethod
```
param\_shapes with static (i.e. `TensorShape`) shapes. (deprecated)
**Deprecated:** THIS FUNCTION IS DEPRECATED. It will be removed after 2021-03-01. Instructions for updating: The `param_static_shapes` method of `tfd.Distribution` is deprecated; use `parameter_properties` instead.
This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Assumes that the sample's shape is known statically.
Subclasses should override class method `_param_shapes` to return constant-valued tensors when constant values are fed.
| Args | |
|---|---|
| `sample_shape` | `TensorShape` or python list/tuple. Desired shape of a call to `sample()`. |
| Returns |
|---|
| `dict` of parameter name to `TensorShape`. |
| Raises | |
|---|---|
| `ValueError` | if `sample_shape` is a `TensorShape` and is not fully defined. |
### `parameter_properties`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L655-L699)
```
@classmethod
```
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution's `Tensor`\-valued constructor arguments.
Distribution subclasses are not required to implement `_parameter_properties`, so this method may raise `NotImplementedError`. Providing a `_parameter_properties` implementation enables several advanced features, including:
- Distribution batch slicing (`sliced_distribution = distribution[i:j]`).
- Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly.
- Automatic instantiation of the distribution within TFP's internal property tests.
- Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.
In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map).
| Args | |
|---|---|
| `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. |
| `num_classes` | Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. |
| Returns | |
|---|---|
| `parameter_properties` | A `str ->`tfp.python.internal.parameter\_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. |
| Raises | |
|---|---|
| `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. |
### `prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1303-L1315)
```
prob(
value, name='prob', **kwargs
)
```
Probability density/mass function.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `quantile`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1555-L1573)
```
quantile(
value, name='quantile', **kwargs
)
```
Quantile function. Aka 'inverse cdf' or 'percent point function'.
Given random variable `X` and `p in [0, 1]`, the `quantile` is:
```
quantile(p) := x such that P[X <= x] == p
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `quantile` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `sample`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1189-L1205)
```
sample(
sample_shape=(), seed=None, name='sample', **kwargs
)
```
Generate samples of the specified shape.
Note that a call to `sample()` without arguments will generate a single sample.
| Args | |
|---|---|
| `sample_shape` | 0D or 1D `int32` `Tensor`. Shape of the generated samples. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. |
| `name` | name to give to the op. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `samples` | a `Tensor` with prepended dimensions `sample_shape`. |
### `stddev`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1613-L1642)
```
stddev(
name='stddev', **kwargs
)
```
Standard deviation.
Standard deviation is defined as,
```
stddev = E[(X - E[X])**2]**0.5
```
where `X` is the random variable associated with this distribution, `E` denotes expectation, and `stddev.shape = batch_shape + event_shape`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `stddev` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. |
### `survival_function`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1498-L1518)
```
survival_function(
value, name='survival_function', **kwargs
)
```
Survival function.
Given random variable `X`, the survival function is defined:
```
survival_function(x) = P[X > x]
= 1 - P[X <= x]
= 1 - cdf(x).
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns |
|---|
| `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `unnormalized_log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1335-L1357)
```
unnormalized_log_prob(
value, name='unnormalized_log_prob', **kwargs
)
```
Potentially unnormalized log probability density/mass function.
This function is similar to `log_prob`, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls `log_prob`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `unnormalized_log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `variance`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1579-L1607)
```
variance(
name='variance', **kwargs
)
```
Variance.
Variance is defined as,
```
Var = E[(X - E[X])**2]
```
where `X` is the random variable associated with this distribution, `E` denotes expectation, and `Var.shape = batch_shape + event_shape`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `variance` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. |
### `with_name_scope`
```
@classmethod
```
Decorator to automatically enter the module name scope.
```
class MyModule(tf.Module):
@tf.Module.with_name_scope
def __call__(self, x):
if not hasattr(self, 'w'):
self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
return tf.matmul(x, self.w)
```
Using the above module would produce [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose names included the module name:
```
mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>
```
| Args | |
|---|---|
| `method` | The method to wrap. |
| Returns |
|---|
| The original method wrapped such that it enters the module's name scope. |
### `__getitem__`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L825-L852)
```
__getitem__(
slices
)
```
Slices the batch axes of this distribution, returning a new instance.
```
b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape # => [3, 1, 5, 2, 4]
x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.batch_shape # => [4, 5, 3]
mvn.event_shape # => [2]
mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
mvn2.batch_shape # => [4, 2, 3, 1]
mvn2.event_shape # => [2]
```
| Args | |
|---|---|
| `slices` | slices from the \[\] operator |
| Returns | |
|---|---|
| `dist` | A new `tfd.Distribution` instance with sliced parameters. |
### `__iter__`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L854-L855)
```
__iter__()
```
Except as otherwise noted, the content of this page is licensed under the [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/), and code samples are licensed under the [Apache 2.0 License](https://www.apache.org/licenses/LICENSE-2.0). For details, see the [Google Developers Site Policies](https://developers.google.com/site-policies). Java is a registered trademark of Oracle and/or its affiliates.
Last updated 2023-11-21 UTC.
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| Readable Markdown | A mixture of a point-mass and another distribution.
Inherits From: [`Mixture`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Mixture), [`AutoCompositeTensorDistribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/AutoCompositeTensorDistribution), [`Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution), [`AutoCompositeTensor`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor)
```
tfp.distributions.Inflated(
distribution,
inflated_loc_logits=None,
inflated_loc_probs=None,
inflated_loc=0.0,
inflated_loc_atol=None,
inflated_loc_rtol=None,
validate_args=False,
allow_nan_stats=True,
name='Inflated'
)
```
Under the hood, this is implemented as a mixture.Mixture, and so supports all of the methods of that class.
\### Examples:
```
zinb = Inflated(
tfd.NegativeBinomial(5.0, probs=0.1), inflated_loc_prob=0.2)
sample = zinb.sample(seed=jax.random.PRNGKey(0))
```
If `distribution` is a `CompositeTensor`s, then the resulting `Inflated` instance is a `CompositeTensor` as well. Otherwise, a non-`CompositeTensor` `_Inflated` instance is created instead. Distribution subclasses that inherit from `Inflated` will also inherit from `CompositeTensor`.
| Args | |
|---|---|
| `distribution` | The tfp.Distribution to combine with a point mass at x. This code is intended to be used only with discrete distributions; when used with continuous distributions sampling will work but log\_probs will be a sum of values with different units. |
| `inflated_loc_logits` | A scalar or tensor containing the excess log-odds for the point mass at inflated\_loc. Only one of `inflated_loc_probs` or `inflated_loc_logits` should be passed in. |
| `inflated_loc_probs` | A scalar or tensor containing the mixture weights for the point mass at inflated\_loc. Only one of `inflated_loc_probs` or `inflated_loc_logits` should be passed in. |
| `inflated_loc` | A scalar or tensor containing the locations of the point mass component of the mixture. |
| `inflated_loc_atol` | Non-negative `Tensor` of same `dtype` as `inflated_loc` and broadcastable shape. The absolute tolerance for comparing closeness to `inflated_loc`. Default is `0`. |
| `inflated_loc_rtol` | Non-negative `Tensor` of same `dtype` as `inflated_loc` and broadcastable shape. The relative tolerance for comparing closeness to `inflated_loc`. Default is `0`. |
| `validate_args` | If true, inconsistent batch or event sizes raise a runtime error. |
| `allow_nan_stats` | If false, any undefined statistics for any batch memeber raise an exception. |
| `name` | An optional name for the distribution. |
| Attributes | |
|---|---|
| `allow_nan_stats` | Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E\[(X - mean)\*\*2\] is also undefined. |
| `batch_shape` | Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution. |
| `cat` | |
| `components` | |
| `distribution` | The distribution used for the non-inflated part. |
| `dtype` | The `DType` of `Tensor`s handled by this `Distribution`. |
| `event_shape` | Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown. |
| `experimental_is_sharded` | |
| `experimental_shard_axis_names` | The list or structure of lists of active shard axis names. |
| `inflated_loc` | The location to add probability mass to. |
| `inflated_loc_logits` | The log-odds for the point mass part of the distribution. |
| `inflated_loc_probs` | The mixture weight(s) for the point mass part of the distribution. |
| `name` | Name prepended to all ops created by this `Distribution`. |
| `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. |
| `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules. |
| `num_components` | |
| `parameters` | Dictionary of parameters used to instantiate this `Distribution`. |
| `reparameterization_type` | Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `tfd.FULLY_REPARAMETERIZED` or `tfd.NOT_REPARAMETERIZED`. |
| `submodules` | Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). |
| `trainable_variables` | Sequence of trainable variables owned by this module and its submodules. |
| `validate_args` | Python `bool` indicating possibly expensive checks are enabled. |
| `variables` | Sequence of variables owned by this module and its submodules. |
## Methods
### `batch_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L992-L1030)
```
batch_shape_tensor(
name='batch_shape_tensor'
)
```
Shape of a single sample from a single event index as a 1-D `Tensor`.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
| Args | |
|---|---|
| `name` | name to give to the op |
| Returns | |
|---|---|
| `batch_shape` | `Tensor`. |
### `cdf`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1411-L1429)
```
cdf(
value, name='cdf', **kwargs
)
```
Cumulative distribution function.
Given random variable `X`, the cumulative distribution function `cdf` is:
```
cdf(x) := P[X <= x]
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `cdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `copy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L896-L924)
```
copy(
**override_parameters_kwargs
)
```
Creates a deep copy of the distribution.
| Args | |
|---|---|
| `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. |
| Returns | |
|---|---|
| `distribution` | A new instance of `type(self)` initialized from the union of self.parameters and override\_parameters\_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. |
### `covariance`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1648-L1686)
```
covariance(
name='covariance', **kwargs
)
```
Covariance.
Covariance is (possibly) defined only for non-scalar-event distributions.
For example, for a length-`k`, vector-valued distribution, it is calculated as,
```
Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
```
where `Cov` is a (batch of) `k x k` matrix, `0 <= (i, j) < k`, and `E` denotes expectation.
Alternatively, for non-vector, multivariate distributions (e.g., matrix-valued, Wishart), `Covariance` shall return a (batch of) matrices under some vectorization of the events, i.e.,
```
Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
```
where `Cov` is a (batch of) `k' x k'` matrices, `0 <= (i, j) < k' = reduce_prod(event_shape)`, and `Vec` is some function mapping indices of this distribution's event dimensions to indices of a length-`k'` vector.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `covariance` | Floating-point `Tensor` with shape `[B1, ..., Bn, k', k']` where the first `n` dimensions are batch coordinates and `k' = reduce_prod(self.event_shape)`. |
### `cross_entropy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1701-L1724)
```
cross_entropy(
other, name='cross_entropy'
)
```
Computes the (Shannon) cross entropy.
Denote this distribution (`self`) by `P` and the `other` distribution by `Q`. Assuming `P, Q` are absolutely continuous with respect to one another and permit densities `p(x) dr(x)` and `q(x) dr(x)`, (Shannon) cross entropy is defined as:
```
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
```
where `F` denotes the support of the random variable `X ~ P`.
| Args | |
|---|---|
| `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. |
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `cross_entropy` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of (Shannon) cross entropy. |
### `entropy`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1524-L1527)
```
entropy(
name='entropy', **kwargs
)
```
Shannon entropy in nats.
### `entropy_lower_bound`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/mixture.py#L344-L390)
```
entropy_lower_bound(
name='entropy_lower_bound'
)
```
A lower bound on the entropy of this mixture model.
The bound below is not always very tight, and its usefulness depends on the mixture probabilities and the components in use.
A lower bound is useful for ELBO when the `Mixture` is the variational distribution:
\\( \\log p(x) \>= ELBO = \\int q(z) \\log p(x, z) dz + H\[q\] \\)
where \\( p \\) is the prior distribution, \\( q \\) is the variational, and \\( H\[q\] \\) is the entropy of \\( q \\). If there is a lower bound \\( G\[q\] \\) such that \\( H\[q\] \\geq G\[q\] \\) then it can be used in place of \\( H\[q\] \\).
For a mixture of distributions \\( q(Z) = \\sum\_i c\_i q\_i(Z) \\) with \\( \\sum\_i c\_i = 1 \\), by the concavity of \\( f(x) = -x \\log x \\), a simple lower bound is:
\\( \\begin{align} H\[q\] & = - \\int q(z) \\log q(z) dz \\\\\\ & = - \\int (\\sum\_i c\_i q\_i(z)) \\log(\\sum\_i c\_i q\_i(z)) dz \\\\\\ & \\geq - \\sum\_i c\_i \\int q\_i(z) \\log q\_i(z) dz \\\\\\ & = \\sum\_i c\_i H\[q\_i\] \\end{align} \\)
This is the term we calculate below for \\( G\[q\] \\).
| Args | |
|---|---|
| `name` | A name for this operation (optional). |
| Returns |
|---|
| A lower bound on the Mixture's entropy. |
### `event_shape_tensor`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1099-L1125)
```
event_shape_tensor(
name='event_shape_tensor'
)
```
Shape of a single sample from a single batch as a 1-D int32 `Tensor`.
| Args | |
|---|---|
| `name` | name to give to the op |
| Returns | |
|---|---|
| `event_shape` | `Tensor`. |
### `experimental_default_event_space_bijector`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1768-L1797)
```
experimental_default_event_space_bijector(
*args, **kwargs
)
```
Bijector mapping the reals (R\*\*n) to the event space of the distribution.
Distributions with continuous support may implement `_default_event_space_bijector` which returns a subclass of [`tfp.bijectors.Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) that maps R\*\*n to the distribution's event space. For example, the default bijector for the `Beta` distribution is [`tfp.bijectors.Sigmoid()`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Sigmoid), which maps the real line to `[0, 1]`, the support of the `Beta` distribution. The default bijector for the `CholeskyLKJ` distribution is [`tfp.bijectors.CorrelationCholesky`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/CorrelationCholesky), which maps R^(k \* (k-1) // 2) to the submanifold of k x k lower triangular matrices with ones along the diagonal.
The purpose of `experimental_default_event_space_bijector` is to enable gradient descent in an unconstrained space for Variational Inference and Hamiltonian Monte Carlo methods. Some effort has been made to choose bijectors such that the tails of the distribution in the unconstrained space are between Gaussian and Exponential.
For distributions with discrete event space, or for which TFP currently lacks a suitable bijector, this function returns `None`.
| Args | |
|---|---|
| `*args` | Passed to implementation `_default_event_space_bijector`. |
| `**kwargs` | Passed to implementation `_default_event_space_bijector`. |
| Returns | |
|---|---|
| `event_space_bijector` | `Bijector` instance or `None`. |
### `experimental_fit`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1799-L1847)
```
@classmethod
```
Instantiates a distribution that maximizes the likelihood of `x`.
| Args | |
|---|---|
| `value` | a `Tensor` valid sample from this distribution family. |
| `sample_ndims` | Positive `int` Tensor number of leftmost dimensions of `value` that index i.i.d. samples. Default value: `1`. |
| `validate_args` | Python `bool`, default `False`. When `True`, distribution parameters are checked for validity despite possibly degrading runtime performance. When `False`, invalid inputs may silently render incorrect outputs. Default value: `False`. |
| `**init_kwargs` | Additional keyword arguments passed through to `cls.__init__`. These take precedence in case of collision with the fitted parameters; for example, `tfd.Normal.experimental_fit([1., 1.], scale=20.)` returns a Normal distribution with `scale=20.` rather than the maximum likelihood parameter `scale=0.`. |
| Returns | |
|---|---|
| `maximum_likelihood_instance` | instance of `cls` with parameters that maximize the likelihood of `value`. |
### `experimental_local_measure`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1872-L1914)
```
experimental_local_measure(
value, backward_compat=False, **kwargs
)
```
Returns a log probability density together with a `TangentSpace`.
A `TangentSpace` allows us to calculate the correct push-forward density when we apply a transformation to a `Distribution` on a strict submanifold of R^n (typically via a `Bijector` in the `TransformedDistribution` subclass). The density correction uses the basis of the tangent space.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `backward_compat` | `bool` specifying whether to fall back to returning `FullSpace` as the tangent space, and representing R^n with the standard basis. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `log_prob` | a `Tensor` representing the log probability density, of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
| `tangent_space` | a `TangentSpace` object (by default `FullSpace`) representing the tangent space to the manifold at `value`. |
| Raises |
|---|
| UnspecifiedTangentSpaceError if `backward_compat` is False and the `_experimental_tangent_space` attribute has not been defined. |
### `experimental_sample_and_log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1229-L1259)
```
experimental_sample_and_log_prob(
sample_shape=(), seed=None, name='sample_and_log_prob', **kwargs
)
```
Samples from this distribution and returns the log density of the sample.
The default implementation simply calls `sample` and `log_prob`:
```
def _sample_and_log_prob(self, sample_shape, seed, **kwargs):
x = self.sample(sample_shape=sample_shape, seed=seed, **kwargs)
return x, self.log_prob(x, **kwargs)
```
However, some subclasses may provide more efficient and/or numerically stable implementations.
| Args | |
|---|---|
| `sample_shape` | integer `Tensor` desired shape of samples to draw. Default value: `()`. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. Default value: `None`. |
| `name` | name to give to the op. Default value: `'sample_and_log_prob'`. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `samples` | a `Tensor`, or structure of `Tensor`s, with prepended dimensions `sample_shape`. |
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `is_scalar_batch`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1156-L1168)
```
is_scalar_batch(
name='is_scalar_batch'
)
```
Indicates that `batch_shape == []`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `is_scalar_batch` | `bool` scalar `Tensor`. |
### `is_scalar_event`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1142-L1154)
```
is_scalar_event(
name='is_scalar_event'
)
```
Indicates that `event_shape == []`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `is_scalar_event` | `bool` scalar `Tensor`. |
### `kl_divergence`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1730-L1761)
```
kl_divergence(
other, name='kl_divergence'
)
```
Computes the Kullback--Leibler divergence.
Denote this distribution (`self`) by `p` and the `other` distribution by `q`. Assuming `p, q` are absolutely continuous with respect to reference measure `r`, the KL divergence is defined as:
```
KL[p, q] = E_p[log(p(X)/q(X))]
= -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
= H[p, q] - H[p]
```
where `F` denotes the support of the random variable `X ~ p`, `H[., .]` denotes (Shannon) cross entropy, and `H[.]` denotes (Shannon) entropy.
| Args | |
|---|---|
| `other` | [`tfp.distributions.Distribution`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Distribution) instance. |
| `name` | Python `str` prepended to names of ops created by this function. |
| Returns | |
|---|---|
| `kl_divergence` | `self.dtype` `Tensor` with shape `[B1, ..., Bn]` representing `n` different calculations of the Kullback-Leibler divergence. |
### `log_cdf`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1373-L1395)
```
log_cdf(
value, name='log_cdf', **kwargs
)
```
Log cumulative distribution function.
Given random variable `X`, the cumulative distribution function `cdf` is:
```
log_cdf(x) := Log[ P[X <= x] ]
```
Often, a numerical approximation can be used for `log_cdf(x)` that yields a more accurate answer than simply taking the logarithm of the `cdf` when `x << -1`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `logcdf` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1275-L1287)
```
log_prob(
value, name='log_prob', **kwargs
)
```
Log probability density/mass function.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `log_survival_function`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1452-L1476)
```
log_survival_function(
value, name='log_survival_function', **kwargs
)
```
Log survival function.
Given random variable `X`, the survival function is defined:
```
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
```
Typically, different numerical approximations can be used for the log survival function, which are more accurate than `1 - cdf(x)` when `x >> 1`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns |
|---|
| `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `mean`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1533-L1536)
```
mean(
name='mean', **kwargs
)
```
Mean.
### `mode`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1692-L1695)
```
mode(
name='mode', **kwargs
)
```
Mode.
### `param_shapes`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L701-L727)
```
@classmethod
```
Shapes of parameters given the desired shape of a call to `sample()`. (deprecated)
This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`.
Subclasses should override class method `_param_shapes`.
| Args | |
|---|---|
| `sample_shape` | `Tensor` or python list/tuple. Desired shape of a call to `sample()`. |
| `name` | name to prepend ops with. |
| Returns |
|---|
| `dict` of parameter name to `Tensor` shapes. |
### `param_static_shapes`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L729-L769)
```
@classmethod
```
param\_shapes with static (i.e. `TensorShape`) shapes. (deprecated)
This is a class method that describes what key/value arguments are required to instantiate the given `Distribution` so that a particular shape is returned for that instance's call to `sample()`. Assumes that the sample's shape is known statically.
Subclasses should override class method `_param_shapes` to return constant-valued tensors when constant values are fed.
| Args | |
|---|---|
| `sample_shape` | `TensorShape` or python list/tuple. Desired shape of a call to `sample()`. |
| Returns |
|---|
| `dict` of parameter name to `TensorShape`. |
| Raises | |
|---|---|
| `ValueError` | if `sample_shape` is a `TensorShape` and is not fully defined. |
### `parameter_properties`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L655-L699)
```
@classmethod
```
Returns a dict mapping constructor arg names to property annotations.
This dict should include an entry for each of the distribution's `Tensor`\-valued constructor arguments.
Distribution subclasses are not required to implement `_parameter_properties`, so this method may raise `NotImplementedError`. Providing a `_parameter_properties` implementation enables several advanced features, including:
- Distribution batch slicing (`sliced_distribution = distribution[i:j]`).
- Automatic inference of `_batch_shape` and `_batch_shape_tensor`, which must otherwise be computed explicitly.
- Automatic instantiation of the distribution within TFP's internal property tests.
- Automatic construction of 'trainable' instances of the distribution using appropriate bijectors to avoid violating parameter constraints. This enables the distribution family to be used easily as a surrogate posterior in variational inference.
In the future, parameter property annotations may enable additional functionality; for example, returning Distribution instances from [`tf.vectorized_map`](https://www.tensorflow.org/api_docs/python/tf/vectorized_map).
| Args | |
|---|---|
| `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. |
| `num_classes` | Optional `int` `Tensor` number of classes to assume when inferring the shape of parameters for categorical-like distributions. Otherwise ignored. |
| Returns | |
|---|---|
| `parameter_properties` | A `str ->`tfp.python.internal.parameter\_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. |
| Raises | |
|---|---|
| `NotImplementedError` | if the distribution class does not implement `_parameter_properties`. |
### `prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1303-L1315)
```
prob(
value, name='prob', **kwargs
)
```
Probability density/mass function.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `quantile`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1555-L1573)
```
quantile(
value, name='quantile', **kwargs
)
```
Quantile function. Aka 'inverse cdf' or 'percent point function'.
Given random variable `X` and `p in [0, 1]`, the `quantile` is:
```
quantile(p) := x such that P[X <= x] == p
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `quantile` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `sample`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1189-L1205)
```
sample(
sample_shape=(), seed=None, name='sample', **kwargs
)
```
Generate samples of the specified shape.
Note that a call to `sample()` without arguments will generate a single sample.
| Args | |
|---|---|
| `sample_shape` | 0D or 1D `int32` `Tensor`. Shape of the generated samples. |
| `seed` | PRNG seed; see [`tfp.random.sanitize_seed`](https://www.tensorflow.org/probability/api_docs/python/tfp/random/sanitize_seed) for details. |
| `name` | name to give to the op. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `samples` | a `Tensor` with prepended dimensions `sample_shape`. |
### `stddev`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1613-L1642)
```
stddev(
name='stddev', **kwargs
)
```
Standard deviation.
Standard deviation is defined as,
```
stddev = E[(X - E[X])**2]**0.5
```
where `X` is the random variable associated with this distribution, `E` denotes expectation, and `stddev.shape = batch_shape + event_shape`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `stddev` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. |
### `survival_function`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1498-L1518)
```
survival_function(
value, name='survival_function', **kwargs
)
```
Survival function.
Given random variable `X`, the survival function is defined:
```
survival_function(x) = P[X > x]
= 1 - P[X <= x]
= 1 - cdf(x).
```
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns |
|---|
| `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `unnormalized_log_prob`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1335-L1357)
```
unnormalized_log_prob(
value, name='unnormalized_log_prob', **kwargs
)
```
Potentially unnormalized log probability density/mass function.
This function is similar to `log_prob`, but does not require that the return value be normalized. (Normalization here refers to the total integral of probability being one, as it should be by definition for any probability distribution.) This is useful, for example, for distributions where the normalization constant is difficult or expensive to compute. By default, this simply calls `log_prob`.
| Args | |
|---|---|
| `value` | `float` or `double` `Tensor`. |
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `unnormalized_log_prob` | a `Tensor` of shape `sample_shape(x) + self.batch_shape` with values of type `self.dtype`. |
### `variance`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L1579-L1607)
```
variance(
name='variance', **kwargs
)
```
Variance.
Variance is defined as,
```
Var = E[(X - E[X])**2]
```
where `X` is the random variable associated with this distribution, `E` denotes expectation, and `Var.shape = batch_shape + event_shape`.
| Args | |
|---|---|
| `name` | Python `str` prepended to names of ops created by this function. |
| `**kwargs` | Named arguments forwarded to subclass implementation. |
| Returns | |
|---|---|
| `variance` | Floating-point `Tensor` with shape identical to `batch_shape + event_shape`, i.e., the same shape as `self.mean()`. |
### `with_name_scope`
```
@classmethod
```
Decorator to automatically enter the module name scope.
```
class MyModule(tf.Module):
@tf.Module.with_name_scope
def __call__(self, x):
if not hasattr(self, 'w'):
self.w = tf.Variable(tf.random.normal([x.shape[1], 3]))
return tf.matmul(x, self.w)
```
Using the above module would produce [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose names included the module name:
```
mod = MyModule()
mod(tf.ones([1, 2]))
<tf.Tensor: shape=(1, 3), dtype=float32, numpy=..., dtype=float32)>
mod.w
<tf.Variable 'my_module/Variable:0' shape=(2, 3) dtype=float32,
numpy=..., dtype=float32)>
```
| Args | |
|---|---|
| `method` | The method to wrap. |
| Returns |
|---|
| The original method wrapped such that it enters the module's name scope. |
### `__getitem__`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L825-L852)
```
__getitem__(
slices
)
```
Slices the batch axes of this distribution, returning a new instance.
```
b = tfd.Bernoulli(logits=tf.zeros([3, 5, 7, 9]))
b.batch_shape # => [3, 5, 7, 9]
b2 = b[:, tf.newaxis, ..., -2:, 1::2]
b2.batch_shape # => [3, 1, 5, 2, 4]
x = tf.random.normal([5, 3, 2, 2])
cov = tf.matmul(x, x, transpose_b=True)
chol = tf.linalg.cholesky(cov)
loc = tf.random.normal([4, 1, 3, 1])
mvn = tfd.MultivariateNormalTriL(loc, chol)
mvn.batch_shape # => [4, 5, 3]
mvn.event_shape # => [2]
mvn2 = mvn[:, 3:, ..., ::-1, tf.newaxis]
mvn2.batch_shape # => [4, 2, 3, 1]
mvn2.event_shape # => [2]
```
| Args | |
|---|---|
| `slices` | slices from the \[\] operator |
| Returns | |
|---|---|
| `dist` | A new `tfd.Distribution` instance with sliced parameters. |
### `__iter__`
[View source](https://github.com/tensorflow/probability/blob/v0.23.0/tensorflow_probability/python/distributions/distribution.py#L854-L855)
```
__iter__()
``` |
| Shard | 168 (laksa) |
| Root Hash | 12537842311192732768 |
| Unparsed URL | org,tensorflow!www,/probability/api_docs/python/tfp/distributions/Inflated s443 |