Unverified50% confidenceFactExact time
The entropy rate is defined as H(X) = lim (1/n) H(X_1,...,X_n), representing the average amount of information carried per symbol.
1
Sources
50%
Confidence
Long-term
Relevance
8/6/2026
First Seen
Sources
马尔可夫链熵率详解：公式推导与序列建模应用
Related Claims
UnverifiedUnder the uniform transition case, the entropy rate of a Markov chain reaches its maximum value of log N, while under the deterministic transition case the entropy rate is 0.71% similarUnverifiedFinite-sample estimation of entropy rate faces a systematic negative bias problem, where plug-in estimators tend to underestimate the true entropy; this can be compensated using the Miller-Madow correction by adding a (k-1)/(2N) term.65% similarPartially VerifiedThe more certain a distribution is, the lower its entropy and the shorter the required encoding; the more random a distribution is (such as a uniform distribution), the higher its entropy.63% similarUnverifiedShannon estimated the information entropy of English to be approximately 1–1.5 bits per character, far below the theoretical maximum.62% similarUnverifiedBecause H(p) is a model-independent constant, minimizing cross-entropy is equivalent to minimizing KL divergence; this equivalence is mathematically exact.61% similar
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