Getting Started Guide

Contents

Logistic Loss

Logistic loss is an objective function being minimized in the process of logistic regression training when a dependent variable takes only one of two values, "0" and "1".
Given
n
feature vectors X = { x
1
= (x
11
,…,x
1p
), ..., x
n
= (x
n 1
,…,x
n p
) } of
n
p
-dimensional feature vectors
,
a vector of class labels
y
= (
y
1
,…,
y
n
) , where
y
i
∈ {0, 1} describes the class to which the feature vector
x
i
belongs, the logistic loss objective function
has a format
where:
  • with
For a given set of the indices I = {
i
1
,
i
2
, ... ,
i
m
}, 1 ≤
i
r
n
,
r
∈ {1, ...,
m
}, the value and the gradient of the sum of functions in the argument x respectively have the format:
  • , where
    ,
For more details, see [ Hastie2009 ]

Product and Performance Information

1

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