Cross Entropy

In information theory, the cross entropy between two probability distributions measures the average number of bits needed to identify an event from a set of possibilities, if a coding scheme is used based on a given probability distribution, rather than the "true" distribution .

The cross entropy for two distributions and over the same probability space is thus defined as follows:

,

where is the entropy of, and is the Kullback-Leibler divergence of from (also known as the relative entropy).

For discrete and this means

The situation for continuous distributions is analogous:

NB: The notation is sometimes used for both the cross entropy as well as the joint entropy of and .

Read more about Cross Entropy:  Motivation, Estimation, Cross-entropy Minimization

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