Cross Entropy Objective Function

f(y) = a·log(y) + b·log(1 − y)
3.0
7.0
Maximum at y = 0.300, f(y) = -2.303

About the Cross Entropy Objective

This function represents a weighted log-likelihood commonly used in machine learning, particularly in binary classification.

• The maximum occurs at y* = a/(a+b)

• When a > b, the maximum shifts toward y = 1

• When b > a, the maximum shifts toward y = 0

• The function is undefined at y = 0 when a > 0 and at y = 1 when b > 0