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 rn , 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]

For more complete information about compiler optimizations, see our Optimization Notice.
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