Entropy of Hidden Markov Processes via Cycle Expansion |
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Authors: | Armen E Allahverdyan |
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Institution: | (1) Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan, 375036, Armenia |
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Abstract: | Hidden Markov Processes (HMP) is one of the basic tools of the modern probabilistic modeling. The characterization of their
entropy remains however an open problem. Here the entropy of HMP is calculated via the cycle expansion of 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 and the moment-generating function. The latter allows to estimate, via the Chernoff bound, the probabilities of large
deviations for the HMP. More generally, the method offers a representation of the moment-generating function and of the entropy
via convergent series. |
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Keywords: | Hidden Markov processes Entropy Generating function |
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