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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 ...
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 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 ...
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 ...
(Here, I(x) is the self-information, which is the entropy contribution of an individual message, and is the expected value.) A property of entropy is that it is maximized when all the messages in the message space are equiprobable p(x) = 1/n; i.e., most unpredictable, in which case H(X) = log n.
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[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