Developer Guide for Intel® Data Analytics Acceleration Library 2019 Update 1
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
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]