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| Meta Title | Classification: objectives and metrics | CatBoost |
| Meta Description | Objectives and metrics. Used for optimization. Objectives and metrics Logloss. |
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| Boilerpipe Text | Objectives and metrics
Used for optimization
Objectives and metrics
Logloss
−
∑
i
=
1
N
w
i
(
c
i
log
(
p
i
)
+
(
1
−
c
i
)
log
(
1
−
p
i
)
)
∑
i
=
1
N
w
i
\displaystyle\frac{ - \sum\limits_{i=1}^N w_{i}\left(c_i \log(p_{i}) + (1-c_{i}) \log(1 - p_{i})\right)}{\sum\limits_{i = 1}^{N} w_{i}}
Usage information
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
CrossEntropy
−
∑
i
=
1
N
w
i
(
t
i
log
(
p
i
)
+
(
1
−
t
i
)
log
(
1
−
p
i
)
)
∑
i
=
1
N
w
i
\displaystyle\frac{- \sum\limits_{i=1}^N w_{i} \left(t_{i} \log(p_{i}) + (1 - t_{i}) \log(1 - p_{i})\right)}{\sum\limits_{i = 1}^{N} w_{i}}
Usage information
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
Precision
T
P
T
P
+
F
P
\frac{TP}{TP + FP}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
Recall
T
P
T
P
+
F
N
\frac{TP}{TP+FN}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
F
(
1
+
β
2
)
⋅
P
r
e
c
i
s
i
o
n
∗
R
e
c
a
l
l
(
β
2
⋅
P
r
e
c
i
s
i
o
n
)
+
R
e
c
a
l
l
(1 + \beta^2) \cdot \frac{Precision * Recall}{(\beta^2 \cdot Precision) + Recall}
Can't be used for optimization.
See
more
.
User-defined parameters
beta
The
β
\beta
parameter of the F metric.
Valid values are real numbers in the following range:
(
0
;
+
∞
)
(0; +\infty)
.
Default:
This parameter is obligatory (the default value is not defined)
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
F1
2
P
r
e
c
i
s
i
o
n
∗
R
e
c
a
l
l
P
r
e
c
i
s
i
o
n
+
R
e
c
a
l
l
2 \frac{Precision * Recall}{Precision + Recall}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
BalancedAccuracy
1
2
(
T
P
P
+
T
N
N
)
\frac{1}{2} \left(\frac{TP}{P} + \frac{TN}{N} \right)
User-defined parameters:
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
BalancedErrorRate
1
2
(
F
P
T
N
+
F
P
+
F
N
F
N
+
T
P
)
\frac{1}{2} \left( \displaystyle\frac{FP}{TN + FP} + \displaystyle\frac{FN}{FN + TP} \right)
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
MCC
T
P
∗
T
N
−
F
P
∗
F
N
(
T
P
+
F
P
)
(
T
P
+
F
N
)
(
T
N
+
F
P
)
(
T
N
+
F
N
)
\displaystyle\frac{TP * TN - FP * FN}{\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
Accuracy
T
P
+
T
N
∑
i
=
1
N
w
i
\frac{TP + TN}{\sum\limits_{i=1}^{N} w_{i}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
CtrFactor
(
∑
i
=
1
N
w
i
t
i
/
N
)
(
∑
i
=
1
N
w
i
p
i
/
N
)
\displaystyle\frac{\left(\sum\limits_{i = 1}^{N} w_{i} t_{i}/N\right)}{\left(\sum\limits_{i = 1}^{N} w_{i} p_{i} /N\right)}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
AUC
The calculation of this metric is disabled by default for the training dataset to speed up the training. Use the
hints=skip_train~false
parameter to enable the calculation.
Classic
∑
I
(
a
i
,
a
j
)
⋅
w
i
⋅
w
j
∑
w
i
⋅
w
j
\displaystyle\frac{\sum I(a_{i}, a_{j}) \cdot w_{i} \cdot w_{j}} {\sum w_{i} \cdot w_{j}}
The sum is calculated on all pairs of objects
(
i
,
j
)
(i,j)
such that:
t
i
=
0
t_{i} = 0
t
j
=
1
t_{j} = 1
I
(
x
,
y
)
=
{
0
,
x
<
y
0.5
,
x
=
y
1
,
x
>
y
I(x, y) = \begin{cases} 0 { , } & x < y \\ 0.5 { , } & x=y \\ 1 { , } & x>y \end{cases}
Refer to the
Wikipedia article
for details.
If the target type is not binary, then every object with target value
t
t
and weight
w
w
is replaced with two objects for the metric calculation:
o
1
o_{1}
with weight
t
⋅
w
t \cdot w
and target value 1
o
2
o_{2}
with weight
(
1
–
t
)
⋅
w
(1 – t) \cdot w
and target value 0.
Target values must be in the range [0; 1].
Ranking
∑
I
(
a
i
,
a
j
)
⋅
w
i
⋅
w
j
∑
w
i
∗
w
j
\displaystyle\frac{\sum I(a_{i}, a_{j}) \cdot w_{i} \cdot w_{j}} {\sum w_{i} * w_{j}}
The sum is calculated on all pairs of objects
(
i
,
j
)
(i,j)
such that:
t
i
<
t
j
t_{i} < t_{j}
I
(
x
,
y
)
=
{
0
,
x
<
y
0.5
,
x
=
y
1
,
x
>
y
I(x, y) = \begin{cases} 0 { , } & x < y \\ 0.5 { , } & x=y \\ 1 { , } & x>y \end{cases}
User-defined parameters
type
The type of AUC. Defines the metric calculation principles.
Default
:
Ranking
.
Possible values:
Classic
,
Ranking
.
Examples:
AUC:type=Classic
,
AUC:type=Ranking
.
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default
:
False
.
Examples
:
QueryAUC:type=Ranking;use_weights=False
.
QueryAUC
Classic type
∑
q
∑
i
,
j
∈
q
∑
I
(
a
i
,
a
j
)
⋅
w
i
⋅
w
j
∑
q
∑
i
,
j
∈
q
∑
w
i
⋅
w
j
\displaystyle\frac{ \sum_q \sum_{i, j \in q} \sum I(a_{i}, a_{j}) \cdot w_{i} \cdot w_{j}} { \sum_q \sum_{i, j \in q}
\sum w_{i} \cdot w_{j}}
The sum is calculated on all pairs of objects
(
i
,
j
)
(i,j)
such that:
t
i
=
0
t_{i} = 0
t
j
=
1
t_{j} = 1
I
(
x
,
y
)
=
{
0
,
x
<
y
0.5
,
x
=
y
1
,
x
>
y
I(x, y) = \begin{cases} 0 { , } & x < y \\ 0.5 { , } & x=y \\ 1 { , } & x>y \end{cases}
Refer to the
Wikipedia article
for details.
If the target type is not binary, then every object with target value
t
t
and weight
w
w
is replaced with two objects for the metric calculation:
o
1
o_{1}
with weight
t
⋅
w
t \cdot w
and target value 1
o
2
o_{2}
with weight
(
1
–
t
)
⋅
w
(1 – t) \cdot w
and target value 0.
Target values must be in the range [0; 1].
Ranking type
∑
q
∑
i
,
j
∈
q
∑
I
(
a
i
,
a
j
)
⋅
w
i
⋅
w
j
∑
q
∑
i
,
j
∈
q
∑
w
i
∗
w
j
\displaystyle\frac{ \sum_q \sum_{i, j \in q} \sum I(a_{i}, a_{j}) \cdot w_{i} \cdot w_{j}} { \sum_q \sum_{i, j \in q} \sum w_{i} * w_{j}}
The sum is calculated on all pairs of objects
(
i
,
j
)
(i,j)
such that:
t
i
<
t
j
t_{i} < t_{j}
I
(
x
,
y
)
=
{
0
,
x
<
y
0.5
,
x
=
y
1
,
x
>
y
I(x, y) = \begin{cases} 0 { , } & x < y \\ 0.5 { , } & x=y \\ 1 { , } & x>y \end{cases}
Can't be used for optimization.
See
more
.
User-defined parameters
type
The type of QueryAUC. Defines the metric calculation principles.
Default
:
Ranking
.
Possible values
:
Classic
,
Ranking
.
Examples
:
QueryAUC:type=Classic
,
QueryAUC:type=Ranking
.
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default
:
False
.
Examples
:
QueryAUC:type=Ranking;use_weights=False
.
PRAUC
PRAUC is the area under the curve
P
r
e
c
i
s
i
o
n
(
q
)
Precision(q)
vs
R
e
c
a
l
l
(
q
)
Recall(q)
for
q
∈
[
0
,
1
]
q \in [0,1]
where
P
r
e
c
i
s
i
o
n
(
q
)
Precision(q)
and
R
e
c
a
l
l
(
q
)
Recall(q)
are defined as follows.
P
r
e
c
i
s
i
o
n
(
q
)
=
T
P
(
q
)
T
P
(
q
)
+
F
P
(
q
)
,
R
e
c
a
l
l
(
q
)
=
T
P
(
q
)
T
P
(
q
)
+
F
N
(
q
)
Precision(q) = \frac{TP(q)}{TP(q) + FP(q)}, Recall(q) = \frac{TP(q)}{TP(q) + FN(q)}
Above
T
P
(
q
)
TP(q)
,
F
P
(
q
)
FP(q)
,
F
N
(
q
)
FN(q)
are weights of the true positive, false positive, and false negative samples, respectively.
To calculate PRAUC for a binary classification model, specify type
Classic
.
In this case,
T
P
(
q
)
=
∑
w
i
[
p
i
>
q
]
c
i
TP(q)=\sum w_i [p_i > q] c_i
, etc.
To calculate PRAUC for a multi-classification model, specify type
OneVsAll
.
In this case, positive samples are samples having class 0, all other samples are negative, and
T
P
(
q
)
=
∑
w
i
[
p
i
0
>
q
]
[
c
i
=
0
]
TP(q)=\sum w_i [p_{i0} > q] [c_i = 0]
, etc.
type
The type of PRAUC. Defines the metric calculation principles.
Type
Classic
is compatible with binary classification models.
Type
OneVsAll
is compatible with multi-classification models.
Default
:
Classic
.
Possible values
:
Classic
,
OneVsAll
.
Examples
:
PRAUC:type=Classic
,
PRAUC:type=OneVsAll
.
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default
:
False
.
Examples
:
PRAUC:type=Classic;use_weights=False
.
NormalizedGini
See AUC.
2
A
U
C
−
1
2 AUC - 1
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
BrierScore
∑
i
=
1
N
w
i
(
p
i
−
t
i
)
2
∑
i
=
1
N
w
i
\displaystyle\frac{\sum\limits_{i=1}^{N} w_{i}\left(p_{i} - t_{i} \right)^{2}}{\sum\limits_{i=1}^{N} w_{i}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
HingeLoss
∑
i
=
1
N
w
i
m
a
x
{
1
−
t
i
p
i
,
0
}
∑
i
=
1
N
w
i
,
t
i
=
±
1
\displaystyle\frac{\sum\limits_{i=1}^{N} w_{i} max\{1 - t_{i} p_{i}, 0\}}{\sum\limits_{i=1}^{N} w_{i}} , t_{i} = \pm 1
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
HammingLoss
∑
i
=
1
N
w
i
[
[
p
i
>
0.5
]
=
=
t
i
]
]
∑
i
=
1
N
w
i
\displaystyle\frac{\sum\limits_{i = 1}^{N} w_{i} [[p_{i} > 0.5] == t_{i}]]}{\sum\limits_{i=1}^{N} w_{i}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
ZeroOneLoss
1
−
A
c
c
u
r
a
c
y
1 - Accuracy
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
Kappa
1
−
1
−
A
c
c
u
r
a
c
y
1
−
R
A
c
c
u
r
a
c
y
1 - \displaystyle\frac{1 - Accuracy}{1 - RAccuracy}
R
A
c
c
u
r
a
c
y
=
(
T
N
+
F
P
)
(
T
N
+
F
N
)
+
(
F
N
+
T
P
)
(
F
P
+
T
P
)
(
∑
i
=
1
N
w
i
)
2
RAccuracy = \displaystyle\frac{(TN + FP) (TN + FN) + (FN + TP) (FP + TP)}{(\sum\limits_{i=1}^{N} w_{i})^{2}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
WKappa
See the formula on page 3 of the
A note on the linearly weighted kappa coefficient for ordinal scales
paper.
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
LogLikelihoodOfPrediction
The calculation consists of the following steps:
Define the sum of weights (
W
W
) and the mean target (
t
ˉ
\bar{t}
):
W
=
∑
i
w
i
W = \sum\limits_{i} w_{i}
t
ˉ
=
1
W
∑
i
t
i
w
i
\bar{t} = \frac{1}{W} \sum\limits_{i} t_{i} w_{i}
Denote log-likelihood of a constant prediction:
l
l
0
=
∑
i
w
i
(
t
ˉ
⋅
l
o
g
(
t
ˉ
)
+
(
1
−
t
ˉ
)
⋅
l
o
g
(
1
−
t
ˉ
)
)
ll_0 = \sum\limits_{i} w_{i} (\bar{t} \cdot log(\bar{t}) + (1 - \bar{t}) \cdot log(1 - \bar{t}))
Calculate LogLikelihoodOfPrediction (
l
l
p
llp
), which reflects how the likelihood (
l
l
ll
) differs from the constant prediction:
l
l
p
=
l
l
(
t
,
w
)
−
l
l
0
∑
i
t
i
w
i
llp = \displaystyle\frac{ll(t, w) - ll_0}{\sum\limits_{i} t_{i} w_{i}}
Can't be used for optimization.
See
more
.
User-defined parameters
use_weights
Use object/group weights to calculate metrics if the specified value is
true
and set all weights to
1
regardless of the input data if the specified value is
false
.
Default:
true
Used for optimization
Name
Optimization
GPU Support
Logloss
+
+
CrossEntropy
+
+
Precision
-
+
Recall
-
+
F
-
-
F1
-
+
BalancedAccuracy
-
-
BalancedErrorRate
-
-
MCC
-
+
Accuracy
-
+
CtrFactor
-
-
AUC
-
-
QueryAUC
-
-
NormalizedGini
-
-
BrierScore
-
-
HingeLoss
-
-
HammingLoss
-
-
ZeroOneLoss
-
+
Kappa
-
-
WKappa
-
-
LogLikelihoodOfPrediction
-
- |
| Markdown | [](https://catboost.ai/ "CatBoost")
- Installation
- [Overview](https://catboost.ai/docs/en/concepts/en/concepts/installation)
- Python package installation
- CatBoost for Apache Spark installation
- R package installation
- Command-line version binary
- Build from source
- Key Features
- Training parameters
- Python package
- CatBoost for Apache Spark
- R package
- Command-line version
- Applying models
- Objectives and metrics
- [Overview](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions)
- [Variables used in formulas](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-variables-used)
- [Regression](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-regression)
- [Multiregression](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-multiregression)
- [Classification](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification)
- [Multiclassification](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-multiclassification)
- [Multilabel Classification](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-multilabel-classification)
- [Ranking](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-ranking)
- Model analysis
- Data format description
- [Parameter tuning](https://catboost.ai/docs/en/concepts/en/concepts/parameter-tuning)
- [Speeding up the training](https://catboost.ai/docs/en/concepts/en/concepts/speed-up-training)
- Data visualization
- Algorithm details
- [FAQ](https://catboost.ai/docs/en/concepts/en/concepts/faq)
- Educational materials
- [Development and contributions](https://catboost.ai/docs/en/concepts/en/concepts/development-and-contributions)
- [Contacts](https://catboost.ai/docs/en/concepts/en/concepts/contacts)
Classification: objectives and metrics
## In this article:
- [Objectives and metrics](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#objectives-and-metrics)
- [Logloss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Logit)
- [CrossEntropy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CrossEntropy)
- [Precision](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Precision)
- [Recall](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Recall)
- [F](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F)
- [F1](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F1)
- [BalancedAccuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedAccuracy)
- [BalancedErrorRate](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedErrorRate)
- [MCC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#MCC)
- [Accuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Accuracy)
- [CtrFactor](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CtrFactor)
- [AUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#AUC)
- [QueryAUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#QueryAUC)
- [PRAUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#PRAUC)
- [NormalizedGini](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#NormalizedGini)
- [BrierScore](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Brierscore)
- [HingeLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HingeLoss)
- [HammingLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HammingLoss)
- [ZeroOneLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#ZeroOneLoss)
- [Kappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Kappa)
- [WKappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#WKappa)
- [LogLikelihoodOfPrediction](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#LLP)
- [Used for optimization](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information)
1. [Objectives and metrics](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions)
2. Classification
# Classification: objectives and metrics
- [Objectives and metrics](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#objectives-and-metrics)
- [Logloss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Logit)
- [CrossEntropy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CrossEntropy)
- [Precision](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Precision)
- [Recall](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Recall)
- [F](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F)
- [F1](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F1)
- [BalancedAccuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedAccuracy)
- [BalancedErrorRate](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedErrorRate)
- [MCC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#MCC)
- [Accuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Accuracy)
- [CtrFactor](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CtrFactor)
- [AUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#AUC)
- [QueryAUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#QueryAUC)
- [PRAUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#PRAUC)
- [NormalizedGini](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#NormalizedGini)
- [BrierScore](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Brierscore)
- [HingeLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HingeLoss)
- [HammingLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HammingLoss)
- [ZeroOneLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#ZeroOneLoss)
- [Kappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Kappa)
- [WKappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#WKappa)
- [LogLikelihoodOfPrediction](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#LLP)
- [Used for optimization](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information)
- [Objectives and metrics](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#objectives-and-metrics)
- [Used for optimization](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information)
## Objectives and metrics
### Logloss
− ∑ i \= 1 N w i ( c i log ( p i ) \+ ( 1 − c i ) log ( 1 − p i ) ) ∑ i \= 1 N w i \\displaystyle\\frac{ - \\sum\\limits\_{i=1}^N w\_{i}\\left(c\_i \\log(p\_{i}) + (1-c\_{i}) \\log(1 - p\_{i})\\right)}{\\sum\\limits\_{i = 1}^{N} w\_{i}} i\=1∑Nwi−i\=1∑Nwi(cilog(pi)\+(1−ci)log(1−pi))
**Usage information** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### CrossEntropy
− ∑ i \= 1 N w i ( t i log ( p i ) \+ ( 1 − t i ) log ( 1 − p i ) ) ∑ i \= 1 N w i \\displaystyle\\frac{- \\sum\\limits\_{i=1}^N w\_{i} \\left(t\_{i} \\log(p\_{i}) + (1 - t\_{i}) \\log(1 - p\_{i})\\right)}{\\sum\\limits\_{i = 1}^{N} w\_{i}} i\=1∑Nwi−i\=1∑Nwi(tilog(pi)\+(1−ti)log(1−pi))
**Usage information** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Precision
T P T P \+ F P \\frac{TP}{TP + FP} TP\+FPTP
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Recall
T P T P \+ F N \\frac{TP}{TP+FN} TP\+FNTP
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### F
( 1 \+ β 2 ) ⋅ P r e c i s i o n ∗ R e c a l l ( β 2 ⋅ P r e c i s i o n ) \+ R e c a l l (1 + \\beta^2) \\cdot \\frac{Precision \* Recall}{(\\beta^2 \\cdot Precision) + Recall} (1\+β2)⋅(β2⋅Precision)\+RecallPrecision∗Recall
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
beta
The β \\beta β parameter of the F metric.
Valid values are real numbers in the following range: ( 0 ; \+ ∞ ) (0; +\\infty) (0;\+∞).
*Default:* This parameter is obligatory (the default value is not defined)
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### F1
2 P r e c i s i o n ∗ R e c a l l P r e c i s i o n \+ R e c a l l 2 \\frac{Precision \* Recall}{Precision + Recall} 2Precision\+RecallPrecision∗Recall
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BalancedAccuracy
1 2 ( T P P \+ T N N ) \\frac{1}{2} \\left(\\frac{TP}{P} + \\frac{TN}{N} \\right) 21(PTP\+NTN)
User-defined parameters:
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BalancedErrorRate
1 2 ( F P T N \+ F P \+ F N F N \+ T P ) \\frac{1}{2} \\left( \\displaystyle\\frac{FP}{TN + FP} + \\displaystyle\\frac{FN}{FN + TP} \\right) 21(TN\+FPFP\+FN\+TPFN)
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### MCC
T P ∗ T N − F P ∗ F N ( T P \+ F P ) ( T P \+ F N ) ( T N \+ F P ) ( T N \+ F N ) \\displaystyle\\frac{TP \* TN - FP \* FN}{\\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}} (TP\+FP)(TP\+FN)(TN\+FP)(TN\+FN) TP∗TN−FP∗FN
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Accuracy
T P \+ T N ∑ i \= 1 N w i \\frac{TP + TN}{\\sum\\limits\_{i=1}^{N} w\_{i}} i\=1∑NwiTP\+TN
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### CtrFactor
( ∑ i \= 1 N w i t i / N ) ( ∑ i \= 1 N w i p i / N ) \\displaystyle\\frac{\\left(\\sum\\limits\_{i = 1}^{N} w\_{i} t\_{i}/N\\right)}{\\left(\\sum\\limits\_{i = 1}^{N} w\_{i} p\_{i} /N\\right)} (i\=1∑Nwipi/N)(i\=1∑Nwiti/N)
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### AUC
The calculation of this metric is disabled by default for the training dataset to speed up the training. Use the `hints=skip_train~false` parameter to enable the calculation.
#### Classic
∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ w i ⋅ w j \\displaystyle\\frac{\\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} {\\sum w\_{i} \\cdot w\_{j}} ∑wi⋅wj∑I(ai,aj)⋅wi⋅wj
The sum is calculated on all pairs of objects ( i , j ) (i,j) (i,j) such that:
- t
i
\=
0
t\_{i} = 0
ti\=0
- t
j
\=
1
t\_{j} = 1
tj\=1
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
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1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
I(x,y)\=
⎩
⎨
⎧
0,0\.5,1,x\<yx\=yx\>y
Refer to the [Wikipedia article](https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve) for details.
If the target type is not binary, then every object with target value t t t and weight w w w is replaced with two objects for the metric calculation:
- o
1
o\_{1}
o1
with weight
t
⋅
w
t \\cdot w
t⋅w
and target value 1
- o
2
o\_{2}
o2
with weight
(
1
–
t
)
⋅
w
(1 – t) \\cdot w
(1–t)⋅w
and target value 0.
Target values must be in the range \[0; 1\].
#### Ranking
∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ w i ∗ w j \\displaystyle\\frac{\\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} {\\sum w\_{i} \* w\_{j}} ∑wi∗wj∑I(ai,aj)⋅wi⋅wj
The sum is calculated on all pairs of objects ( i , j ) (i,j) (i,j) such that:
- t
i
\<
t
j
t\_{i} \< t\_{j}
ti\<tj
- I
(
x
,
y
)
\=
{
0
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0\.5
,
x
\=
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1
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\>
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I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
I(x,y)\=
⎩
⎨
⎧
0,0\.5,1,x\<yx\=yx\>y
**User-defined parameters**
type
The type of AUC. Defines the metric calculation principles.
*Default*: `Ranking`.
*Possible values:* `Classic`, `Ranking`.
*Examples:* `AUC:type=Classic`, `AUC:type=Ranking`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `QueryAUC:type=Ranking;use_weights=False`.
### QueryAUC
#### Classic type
∑ q ∑ i , j ∈ q ∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ q ∑ i , j ∈ q ∑ w i ⋅ w j \\displaystyle\\frac{ \\sum\_q \\sum\_{i, j \\in q} \\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} { \\sum\_q \\sum\_{i, j \\in q} \\sum w\_{i} \\cdot w\_{j}} ∑q∑i,j∈q∑wi⋅wj∑q∑i,j∈q∑I(ai,aj)⋅wi⋅wj
The sum is calculated on all pairs of objects ( i , j ) (i,j) (i,j) such that:
- t
i
\=
0
t\_{i} = 0
ti\=0
- t
j
\=
1
t\_{j} = 1
tj\=1
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
I(x,y)\=
⎩
⎨
⎧
0,0\.5,1,x\<yx\=yx\>y
Refer to the [Wikipedia article](https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve) for details.
If the target type is not binary, then every object with target value t t t and weight w w w is replaced with two objects for the metric calculation:
- o
1
o\_{1}
o1
with weight
t
⋅
w
t \\cdot w
t⋅w
and target value 1
- o
2
o\_{2}
o2
with weight
(
1
–
t
)
⋅
w
(1 – t) \\cdot w
(1–t)⋅w
and target value 0.
Target values must be in the range \[0; 1\].
#### Ranking type
∑ q ∑ i , j ∈ q ∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ q ∑ i , j ∈ q ∑ w i ∗ w j \\displaystyle\\frac{ \\sum\_q \\sum\_{i, j \\in q} \\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} { \\sum\_q \\sum\_{i, j \\in q} \\sum w\_{i} \* w\_{j}} ∑q∑i,j∈q∑wi∗wj∑q∑i,j∈q∑I(ai,aj)⋅wi⋅wj
The sum is calculated on all pairs of objects ( i , j ) (i,j) (i,j) such that:
- t
i
\<
t
j
t\_{i} \< t\_{j}
ti\<tj
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
I(x,y)\=
⎩
⎨
⎧
0,0\.5,1,x\<yx\=yx\>y
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#optimization).
**User-defined parameters**
type
The type of QueryAUC. Defines the metric calculation principles.
*Default*: `Ranking`.
*Possible values*: `Classic`, `Ranking`.
*Examples*: `QueryAUC:type=Classic`, `QueryAUC:type=Ranking`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `QueryAUC:type=Ranking;use_weights=False`.
### PRAUC
PRAUC is the area under the curve P r e c i s i o n ( q ) Precision(q) Precision(q) vs R e c a l l ( q ) Recall(q) Recall(q) for q ∈ \[ 0 , 1 \] q \\in \[0,1\] q∈\[0,1\] where P r e c i s i o n ( q ) Precision(q) Precision(q) and R e c a l l ( q ) Recall(q) Recall(q) are defined as follows.
P r e c i s i o n ( q ) \= T P ( q ) T P ( q ) \+ F P ( q ) , R e c a l l ( q ) \= T P ( q ) T P ( q ) \+ F N ( q ) Precision(q) = \\frac{TP(q)}{TP(q) + FP(q)}, Recall(q) = \\frac{TP(q)}{TP(q) + FN(q)} Precision(q)\=TP(q)\+FP(q)TP(q),Recall(q)\=TP(q)\+FN(q)TP(q)
Above T P ( q ) TP(q) TP(q), F P ( q ) FP(q) FP(q), F N ( q ) FN(q) FN(q) are weights of the true positive, false positive, and false negative samples, respectively.
To calculate PRAUC for a binary classification model, specify type `Classic`.
In this case, T P ( q ) \= ∑ w i \[ p i \> q \] c i TP(q)=\\sum w\_i \[p\_i \> q\] c\_i TP(q)\=∑wi\[pi\>q\]ci, etc.
To calculate PRAUC for a multi-classification model, specify type `OneVsAll`.
In this case, positive samples are samples having class 0, all other samples are negative, and T P ( q ) \= ∑ w i \[ p i 0 \> q \] \[ c i \= 0 \] TP(q)=\\sum w\_i \[p\_{i0} \> q\] \[c\_i = 0\] TP(q)\=∑wi\[pi0\>q\]\[ci\=0\], etc.
type
The type of PRAUC. Defines the metric calculation principles.
Type `Classic` is compatible with binary classification models.
Type `OneVsAll` is compatible with multi-classification models.
*Default*: `Classic`.
*Possible values*: `Classic`, `OneVsAll`.
*Examples*: `PRAUC:type=Classic`, `PRAUC:type=OneVsAll`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `PRAUC:type=Classic;use_weights=False`.
### NormalizedGini
See AUC.
2 A U C − 1 2 AUC - 1 2AUC−1
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BrierScore
∑ i \= 1 N w i ( p i − t i ) 2 ∑ i \= 1 N w i \\displaystyle\\frac{\\sum\\limits\_{i=1}^{N} w\_{i}\\left(p\_{i} - t\_{i} \\right)^{2}}{\\sum\\limits\_{i=1}^{N} w\_{i}} i\=1∑Nwii\=1∑Nwi(pi−ti)2
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### HingeLoss
∑ i \= 1 N w i m a x { 1 − t i p i , 0 } ∑ i \= 1 N w i , t i \= ± 1 \\displaystyle\\frac{\\sum\\limits\_{i=1}^{N} w\_{i} max\\{1 - t\_{i} p\_{i}, 0\\}}{\\sum\\limits\_{i=1}^{N} w\_{i}} , t\_{i} = \\pm 1 i\=1∑Nwii\=1∑Nwimax{1−tipi,0},ti\=±1
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### HammingLoss
∑ i \= 1 N w i \[ \[ p i \> 0\.5 \] \= \= t i \] \] ∑ i \= 1 N w i \\displaystyle\\frac{\\sum\\limits\_{i = 1}^{N} w\_{i} \[\[p\_{i} \> 0.5\] == t\_{i}\]\]}{\\sum\\limits\_{i=1}^{N} w\_{i}} i\=1∑Nwii\=1∑Nwi\[\[pi\>0\.5\]\==ti\]\]
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### ZeroOneLoss
1 − A c c u r a c y 1 - Accuracy 1−Accuracy
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Kappa
1 − 1 − A c c u r a c y 1 − R A c c u r a c y 1 - \\displaystyle\\frac{1 - Accuracy}{1 - RAccuracy} 1−1−RAccuracy1−Accuracy
R A c c u r a c y \= ( T N \+ F P ) ( T N \+ F N ) \+ ( F N \+ T P ) ( F P \+ T P ) ( ∑ i \= 1 N w i ) 2 RAccuracy = \\displaystyle\\frac{(TN + FP) (TN + FN) + (FN + TP) (FP + TP)}{(\\sum\\limits\_{i=1}^{N} w\_{i})^{2}} RAccuracy\=(i\=1∑Nwi)2(TN\+FP)(TN\+FN)\+(FN\+TP)(FP\+TP)
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### WKappa
See the formula on page 3 of the [A note on the linearly weighted kappa coefficient for ordinal scales](https://orbi.uliege.be/bitstream/2268/2262/1/STATMED-174.pdf) paper.
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### LogLikelihoodOfPrediction
The calculation consists of the following steps:
1. Define the sum of weights (W W W) and the mean target (t ˉ \\bar{t} tˉ):
W \= ∑ i w i W = \\sum\\limits\_{i} w\_{i} W\=i∑wi
t ˉ \= 1 W ∑ i t i w i \\bar{t} = \\frac{1}{W} \\sum\\limits\_{i} t\_{i} w\_{i} tˉ\=W1i∑tiwi
2. Denote log-likelihood of a constant prediction:
l l 0 \= ∑ i w i ( t ˉ ⋅ l o g ( t ˉ ) \+ ( 1 − t ˉ ) ⋅ l o g ( 1 − t ˉ ) ) ll\_0 = \\sum\\limits\_{i} w\_{i} (\\bar{t} \\cdot log(\\bar{t}) + (1 - \\bar{t}) \\cdot log(1 - \\bar{t})) ll0\=i∑wi(tˉ⋅log(tˉ)\+(1−tˉ)⋅log(1−tˉ))
3. Calculate LogLikelihoodOfPrediction (l l p llp llp), which reflects how the likelihood (l l ll ll) differs from the constant prediction:
l l p \= l l ( t , w ) − l l 0 ∑ i t i w i llp = \\displaystyle\\frac{ll(t, w) - ll\_0}{\\sum\\limits\_{i} t\_{i} w\_{i}} llp\=i∑tiwill(t,w)−ll0
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
## Used for optimization
| Name | Optimization | GPU Support |
|---|---|---|
| [Logloss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Logit) | \+ | \+ |
| [CrossEntropy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CrossEntropy) | \+ | \+ |
| [Precision](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Precision) | \- | \+ |
| [Recall](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Recall) | \- | \+ |
| [F](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F) | \- | \- |
| [F1](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#F1) | \- | \+ |
| [BalancedAccuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedAccuracy) | \- | \- |
| [BalancedErrorRate](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#BalancedErrorRate) | \- | \- |
| [MCC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#MCC) | \- | \+ |
| [Accuracy](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Accuracy) | \- | \+ |
| [CtrFactor](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#CtrFactor) | \- | \- |
| [AUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#AUC) | \- | \- |
| [QueryAUC](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#QueryAUC) | \- | \- |
| [NormalizedGini](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#ormalizedGini) | \- | \- |
| [BrierScore](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Brierscore) | \- | \- |
| [HingeLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HingeLoss) | \- | \- |
| [HammingLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#HammingLoss) | \- | \- |
| [ZeroOneLoss](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#ZeroOneLoss) | \- | \+ |
| [Kappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#Kappa) | \- | \- |
| [WKappa](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#WKappa) | \- | \- |
| [LogLikelihoodOfPrediction](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-classification#LLP) | \- | \- |
### Was the article helpful?
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[Multiregression](https://catboost.ai/docs/en/concepts/en/concepts/loss-functions-multiregression)
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 |
| Readable Markdown | - [Objectives and metrics](https://catboost.ai/docs/en/concepts/loss-functions-classification#objectives-and-metrics)
- [Used for optimization](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information)
## Objectives and metrics
### Logloss
− ∑ i \= 1 N w i ( c i log ( p i ) \+ ( 1 − c i ) log ( 1 − p i ) ) ∑ i \= 1 N w i \\displaystyle\\frac{ - \\sum\\limits\_{i=1}^N w\_{i}\\left(c\_i \\log(p\_{i}) + (1-c\_{i}) \\log(1 - p\_{i})\\right)}{\\sum\\limits\_{i = 1}^{N} w\_{i}}
**Usage information** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### CrossEntropy
− ∑ i \= 1 N w i ( t i log ( p i ) \+ ( 1 − t i ) log ( 1 − p i ) ) ∑ i \= 1 N w i \\displaystyle\\frac{- \\sum\\limits\_{i=1}^N w\_{i} \\left(t\_{i} \\log(p\_{i}) + (1 - t\_{i}) \\log(1 - p\_{i})\\right)}{\\sum\\limits\_{i = 1}^{N} w\_{i}}
**Usage information** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Precision
T P T P \+ F P \\frac{TP}{TP + FP}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Recall
T P T P \+ F N \\frac{TP}{TP+FN}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### F
( 1 \+ β 2 ) ⋅ P r e c i s i o n ∗ R e c a l l ( β 2 ⋅ P r e c i s i o n ) \+ R e c a l l (1 + \\beta^2) \\cdot \\frac{Precision \* Recall}{(\\beta^2 \\cdot Precision) + Recall}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
beta
The β \\beta parameter of the F metric.
Valid values are real numbers in the following range: ( 0 ; \+ ∞ ) (0; +\\infty).
*Default:* This parameter is obligatory (the default value is not defined)
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### F1
2 P r e c i s i o n ∗ R e c a l l P r e c i s i o n \+ R e c a l l 2 \\frac{Precision \* Recall}{Precision + Recall}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BalancedAccuracy
1 2 ( T P P \+ T N N ) \\frac{1}{2} \\left(\\frac{TP}{P} + \\frac{TN}{N} \\right)
User-defined parameters:
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BalancedErrorRate
1 2 ( F P T N \+ F P \+ F N F N \+ T P ) \\frac{1}{2} \\left( \\displaystyle\\frac{FP}{TN + FP} + \\displaystyle\\frac{FN}{FN + TP} \\right)
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### MCC
T P ∗ T N − F P ∗ F N ( T P \+ F P ) ( T P \+ F N ) ( T N \+ F P ) ( T N \+ F N ) \\displaystyle\\frac{TP \* TN - FP \* FN}{\\sqrt{(TP + FP)(TP + FN)(TN + FP)(TN + FN)}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Accuracy
T P \+ T N ∑ i \= 1 N w i \\frac{TP + TN}{\\sum\\limits\_{i=1}^{N} w\_{i}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### CtrFactor
( ∑ i \= 1 N w i t i / N ) ( ∑ i \= 1 N w i p i / N ) \\displaystyle\\frac{\\left(\\sum\\limits\_{i = 1}^{N} w\_{i} t\_{i}/N\\right)}{\\left(\\sum\\limits\_{i = 1}^{N} w\_{i} p\_{i} /N\\right)}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### AUC
The calculation of this metric is disabled by default for the training dataset to speed up the training. Use the `hints=skip_train~false` parameter to enable the calculation.
#### Classic
∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ w i ⋅ w j \\displaystyle\\frac{\\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} {\\sum w\_{i} \\cdot w\_{j}}
The sum is calculated on all pairs of objects ( i , j ) (i,j) such that:
- t
i
\=
0
t\_{i} = 0
- t
j
\=
1
t\_{j} = 1
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
Refer to the [Wikipedia article](https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve) for details.
If the target type is not binary, then every object with target value t t and weight w w is replaced with two objects for the metric calculation:
- o
1
o\_{1}
with weight
t
⋅
w
t \\cdot w
and target value 1
- o
2
o\_{2}
with weight
(
1
–
t
)
⋅
w
(1 – t) \\cdot w
and target value 0.
Target values must be in the range \[0; 1\].
#### Ranking
∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ w i ∗ w j \\displaystyle\\frac{\\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} {\\sum w\_{i} \* w\_{j}}
The sum is calculated on all pairs of objects ( i , j ) (i,j) such that:
- t
i
\<
t
j
t\_{i} \< t\_{j}
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
**User-defined parameters**
type
The type of AUC. Defines the metric calculation principles.
*Default*: `Ranking`.
*Possible values:* `Classic`, `Ranking`.
*Examples:* `AUC:type=Classic`, `AUC:type=Ranking`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `QueryAUC:type=Ranking;use_weights=False`.
### QueryAUC
#### Classic type
∑ q ∑ i , j ∈ q ∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ q ∑ i , j ∈ q ∑ w i ⋅ w j \\displaystyle\\frac{ \\sum\_q \\sum\_{i, j \\in q} \\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} { \\sum\_q \\sum\_{i, j \\in q} \\sum w\_{i} \\cdot w\_{j}}
The sum is calculated on all pairs of objects ( i , j ) (i,j) such that:
- t
i
\=
0
t\_{i} = 0
- t
j
\=
1
t\_{j} = 1
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
Refer to the [Wikipedia article](https://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve) for details.
If the target type is not binary, then every object with target value t t and weight w w is replaced with two objects for the metric calculation:
- o
1
o\_{1}
with weight
t
⋅
w
t \\cdot w
and target value 1
- o
2
o\_{2}
with weight
(
1
–
t
)
⋅
w
(1 – t) \\cdot w
and target value 0.
Target values must be in the range \[0; 1\].
#### Ranking type
∑ q ∑ i , j ∈ q ∑ I ( a i , a j ) ⋅ w i ⋅ w j ∑ q ∑ i , j ∈ q ∑ w i ∗ w j \\displaystyle\\frac{ \\sum\_q \\sum\_{i, j \\in q} \\sum I(a\_{i}, a\_{j}) \\cdot w\_{i} \\cdot w\_{j}} { \\sum\_q \\sum\_{i, j \\in q} \\sum w\_{i} \* w\_{j}}
The sum is calculated on all pairs of objects ( i , j ) (i,j) such that:
- t
i
\<
t
j
t\_{i} \< t\_{j}
- I
(
x
,
y
)
\=
{
0
,
x
\<
y
0\.5
,
x
\=
y
1
,
x
\>
y
I(x, y) = \\begin{cases} 0 { , } & x \< y \\\\ 0.5 { , } & x=y \\\\ 1 { , } & x\>y \\end{cases}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#optimization).
**User-defined parameters**
type
The type of QueryAUC. Defines the metric calculation principles.
*Default*: `Ranking`.
*Possible values*: `Classic`, `Ranking`.
*Examples*: `QueryAUC:type=Classic`, `QueryAUC:type=Ranking`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `QueryAUC:type=Ranking;use_weights=False`.
### PRAUC
PRAUC is the area under the curve P r e c i s i o n ( q ) Precision(q) vs R e c a l l ( q ) Recall(q) for q ∈ \[ 0 , 1 \] q \\in \[0,1\] where P r e c i s i o n ( q ) Precision(q) and R e c a l l ( q ) Recall(q) are defined as follows.
P r e c i s i o n ( q ) \= T P ( q ) T P ( q ) \+ F P ( q ) , R e c a l l ( q ) \= T P ( q ) T P ( q ) \+ F N ( q ) Precision(q) = \\frac{TP(q)}{TP(q) + FP(q)}, Recall(q) = \\frac{TP(q)}{TP(q) + FN(q)}
Above T P ( q ) TP(q), F P ( q ) FP(q), F N ( q ) FN(q) are weights of the true positive, false positive, and false negative samples, respectively.
To calculate PRAUC for a binary classification model, specify type `Classic`.
In this case, T P ( q ) \= ∑ w i \[ p i \> q \] c i TP(q)=\\sum w\_i \[p\_i \> q\] c\_i, etc.
To calculate PRAUC for a multi-classification model, specify type `OneVsAll`.
In this case, positive samples are samples having class 0, all other samples are negative, and T P ( q ) \= ∑ w i \[ p i 0 \> q \] \[ c i \= 0 \] TP(q)=\\sum w\_i \[p\_{i0} \> q\] \[c\_i = 0\], etc.
type
The type of PRAUC. Defines the metric calculation principles.
Type `Classic` is compatible with binary classification models.
Type `OneVsAll` is compatible with multi-classification models.
*Default*: `Classic`.
*Possible values*: `Classic`, `OneVsAll`.
*Examples*: `PRAUC:type=Classic`, `PRAUC:type=OneVsAll`.
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default*: `False`.
*Examples*: `PRAUC:type=Classic;use_weights=False`.
### NormalizedGini
See AUC.
2 A U C − 1 2 AUC - 1
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### BrierScore
∑ i \= 1 N w i ( p i − t i ) 2 ∑ i \= 1 N w i \\displaystyle\\frac{\\sum\\limits\_{i=1}^{N} w\_{i}\\left(p\_{i} - t\_{i} \\right)^{2}}{\\sum\\limits\_{i=1}^{N} w\_{i}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### HingeLoss
∑ i \= 1 N w i m a x { 1 − t i p i , 0 } ∑ i \= 1 N w i , t i \= ± 1 \\displaystyle\\frac{\\sum\\limits\_{i=1}^{N} w\_{i} max\\{1 - t\_{i} p\_{i}, 0\\}}{\\sum\\limits\_{i=1}^{N} w\_{i}} , t\_{i} = \\pm 1
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### HammingLoss
∑ i \= 1 N w i \[ \[ p i \> 0\.5 \] \= \= t i \] \] ∑ i \= 1 N w i \\displaystyle\\frac{\\sum\\limits\_{i = 1}^{N} w\_{i} \[\[p\_{i} \> 0.5\] == t\_{i}\]\]}{\\sum\\limits\_{i=1}^{N} w\_{i}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### ZeroOneLoss
1 − A c c u r a c y 1 - Accuracy
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### Kappa
1 − 1 − A c c u r a c y 1 − R A c c u r a c y 1 - \\displaystyle\\frac{1 - Accuracy}{1 - RAccuracy}
R A c c u r a c y \= ( T N \+ F P ) ( T N \+ F N ) \+ ( F N \+ T P ) ( F P \+ T P ) ( ∑ i \= 1 N w i ) 2 RAccuracy = \\displaystyle\\frac{(TN + FP) (TN + FN) + (FN + TP) (FP + TP)}{(\\sum\\limits\_{i=1}^{N} w\_{i})^{2}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### WKappa
See the formula on page 3 of the [A note on the linearly weighted kappa coefficient for ordinal scales](https://orbi.uliege.be/bitstream/2268/2262/1/STATMED-174.pdf) paper.
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
### LogLikelihoodOfPrediction
The calculation consists of the following steps:
1. Define the sum of weights (W W) and the mean target (t ˉ \\bar{t}):
W \= ∑ i w i W = \\sum\\limits\_{i} w\_{i}
t ˉ \= 1 W ∑ i t i w i \\bar{t} = \\frac{1}{W} \\sum\\limits\_{i} t\_{i} w\_{i}
2. Denote log-likelihood of a constant prediction:
l l 0 \= ∑ i w i ( t ˉ ⋅ l o g ( t ˉ ) \+ ( 1 − t ˉ ) ⋅ l o g ( 1 − t ˉ ) ) ll\_0 = \\sum\\limits\_{i} w\_{i} (\\bar{t} \\cdot log(\\bar{t}) + (1 - \\bar{t}) \\cdot log(1 - \\bar{t}))
3. Calculate LogLikelihoodOfPrediction (l l p llp), which reflects how the likelihood (l l ll) differs from the constant prediction:
l l p \= l l ( t , w ) − l l 0 ∑ i t i w i llp = \\displaystyle\\frac{ll(t, w) - ll\_0}{\\sum\\limits\_{i} t\_{i} w\_{i}}
**Can't be used for optimization.** See [more](https://catboost.ai/docs/en/concepts/loss-functions-classification#usage-information).
**User-defined parameters**
use\_weights
Use object/group weights to calculate metrics if the specified value is "true" and set all weights to "1" regardless of the input data if the specified value is "false".
*Default:* true
## Used for optimization
| Name | Optimization | GPU Support |
|---|---|---|
| [Logloss](https://catboost.ai/docs/en/concepts/loss-functions-classification#Logit) | \+ | \+ |
| [CrossEntropy](https://catboost.ai/docs/en/concepts/loss-functions-classification#CrossEntropy) | \+ | \+ |
| [Precision](https://catboost.ai/docs/en/concepts/loss-functions-classification#Precision) | \- | \+ |
| [Recall](https://catboost.ai/docs/en/concepts/loss-functions-classification#Recall) | \- | \+ |
| [F](https://catboost.ai/docs/en/concepts/loss-functions-classification#F) | \- | \- |
| [F1](https://catboost.ai/docs/en/concepts/loss-functions-classification#F1) | \- | \+ |
| [BalancedAccuracy](https://catboost.ai/docs/en/concepts/loss-functions-classification#BalancedAccuracy) | \- | \- |
| [BalancedErrorRate](https://catboost.ai/docs/en/concepts/loss-functions-classification#BalancedErrorRate) | \- | \- |
| [MCC](https://catboost.ai/docs/en/concepts/loss-functions-classification#MCC) | \- | \+ |
| [Accuracy](https://catboost.ai/docs/en/concepts/loss-functions-classification#Accuracy) | \- | \+ |
| [CtrFactor](https://catboost.ai/docs/en/concepts/loss-functions-classification#CtrFactor) | \- | \- |
| [AUC](https://catboost.ai/docs/en/concepts/loss-functions-classification#AUC) | \- | \- |
| [QueryAUC](https://catboost.ai/docs/en/concepts/loss-functions-classification#QueryAUC) | \- | \- |
| [NormalizedGini](https://catboost.ai/docs/en/concepts/loss-functions-classification#ormalizedGini) | \- | \- |
| [BrierScore](https://catboost.ai/docs/en/concepts/loss-functions-classification#Brierscore) | \- | \- |
| [HingeLoss](https://catboost.ai/docs/en/concepts/loss-functions-classification#HingeLoss) | \- | \- |
| [HammingLoss](https://catboost.ai/docs/en/concepts/loss-functions-classification#HammingLoss) | \- | \- |
| [ZeroOneLoss](https://catboost.ai/docs/en/concepts/loss-functions-classification#ZeroOneLoss) | \- | \+ |
| [Kappa](https://catboost.ai/docs/en/concepts/loss-functions-classification#Kappa) | \- | \- |
| [WKappa](https://catboost.ai/docs/en/concepts/loss-functions-classification#WKappa) | \- | \- |
| [LogLikelihoodOfPrediction](https://catboost.ai/docs/en/concepts/loss-functions-classification#LLP) | \- | \- | |
| Shard | 169 (laksa) |
| Root Hash | 17435841955170310369 |
| Unparsed URL | ai,catboost!/docs/en/concepts/loss-functions-classification s443 |