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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 .
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.
The cross entropy between two probability distributions (p and q) 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 q, rather than the "true" distribution p. The cross entropy for two distributions p and q over the same probability ...
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. Notice, as per property of the Kullback–Leibler divergence, that (;) is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent (and hence observing tells you nothing about ).
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.
The lowest perplexity that had been published on the Brown Corpus (1 million words of American English of varying topics and genres) as of 1992 is indeed about 247 per word/token, corresponding to a cross-entropy of log 2 247 = 7.95 bits per word or 1.75 bits per letter [5] using a trigram model. While this figure represented the state of the ...
Cross-entropy benchmarking (also referred to as XEB) is a quantum benchmarking protocol which can be used to demonstrate quantum supremacy. [1] In XEB, a random quantum circuit is executed on a quantum computer multiple times in order to collect a set of k {\displaystyle k} samples in the form of bitstrings { x 1 , … , x k } {\displaystyle ...
[1]: 68 Put in words, the information entropy of a distribution is less than or equal to its cross entropy with any other distribution . The difference between the two quantities is the Kullback–Leibler divergence or relative entropy, so the inequality can also be written: [2]: 34