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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.
In information theory, the cross-entropy between two probability distributions and , over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution .
Entropy (thermodynamics) Cross entropy – is a measure of the average number of bits needed to identify an event from a set of possibilities between two probability distributions; Entropy (arrow of time) Entropy encoding – a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. Entropy ...
Package-merge algorithm: Optimizes Huffman coding subject to a length restriction on code strings; Shannon–Fano coding; Shannon–Fano–Elias coding: precursor to arithmetic encoding [5] Entropy coding with known entropy characteristics. Golomb coding: form of entropy coding that is optimal for alphabets following geometric distributions
More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...
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 ...
Estimation of distribution algorithms and the Cross-Entropy Method are based on very similar ideas, but estimate (non-incrementally) the covariance matrix by maximizing the likelihood of successful solution points instead of successful search steps.
A higher temperature results in a more uniform output distribution (i.e. with higher entropy; it is "more random"), while a lower temperature results in a sharper output distribution, with one value dominating. In some fields, the base is fixed, corresponding to a fixed scale, [d] while in others the parameter β (or T) is varied.