Shannon Entropy Rate of Hidden Markov Processes

Abstract

Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously complicated, however, even if the chain is finite state: no finite expression for their Shannon entropy rate exists, as the set of their predictive features is generically infinite. As such, to date one cannot make general statements about how random they are nor how structured. Here, we address the first part of this challenge by showing how to efficiently and accurately calculate their entropy rates. We also show how this method gives the minimal set of infinite predictive features. A sequel addresses the challenge's second part on structure.

11 pages, 4 figures; supplementary material 10 pages, 7 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/serhmp.htm

References in corpus (6)

• Information Anatomy of Stochastic Equilibria
• Shannon Entropy Rate of Hidden Markov Processes
• Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes
• Hidden Markov Process: A New Representation, Entropy Rate and Estimation Entropy
• Entropy of Hidden Markov Processes via Cycle Expansion
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