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Cross-entropy can be used to define a loss function in machine learning and optimization. Mao, Mohri, and Zhong (2023) give an extensive analysis of the properties of the family of cross-entropy loss functions in machine learning, including theoretical learning guarantees and extensions to adversarial learning. [3]
Such networks are commonly trained under a log loss (or cross-entropy) regime, giving a non-linear variant of multinomial logistic regression. Since the function maps a vector and a specific index i {\displaystyle i} to a real value, the derivative needs to take the index into account:
The cross-entropy loss is closely related to the Kullback–Leibler divergence between the empirical distribution and the predicted distribution. The cross-entropy loss is ubiquitous in modern deep neural networks .
Torch development moved in 2017 to PyTorch, a ... and the cross-entropy criterion implemented in ClassNLLCriterion. What follows is an example of a Lua ...
In probability theory, statistics, and machine learning, the continuous Bernoulli distribution [1] [2] [3] is a family of continuous probability distributions parameterized by a single shape parameter (,), defined on the unit interval [,], by:
The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: [1] Draw a sample from a probability distribution.
Multinomial logistic regression is known by a variety of other names, including polytomous LR, [2] [3] multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model.
The entropy () thus sets a minimum value for the cross-entropy (,), the expected number of bits required when using a code based on Q rather than P; and the Kullback–Leibler divergence therefore represents the expected number of extra bits that must be transmitted to identify a value x drawn from X, if a code is used corresponding to the ...