Entropy of Hidden Markov Processes via Cycle Expansion - Computer Science > Information TheoryReport as inadecuate




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Abstract: Hidden Markov Processes HMP is one of the basic tools of the modernprobabilistic modeling. The characterization of their entropy remains howeveran open problem. Here the entropy of HMP is calculated via the cycle expansionof the zeta-function, a method adopted from the theory of dynamical systems.For a class of HMP this method produces exact results both for the entropy andthe moment-generating function. The latter allows to estimate, via the Chernoffbound, the probabilities of large deviations for the HMP. More generally, themethod offers a representation of the moment-generating function and of theentropy via convergent series.



Author: Armen E. Allahverdyan

Source: https://arxiv.org/



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