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, artificial intelligence. The hidden processes they generate notoriously complicated, however, even if the chain is finite state: no expression for their Shannon entropy rate exists, as set predictive features generically infinite. As such, date one cannot make general statements about how random nor structured. Here, we address first part this challenge by showing efficiently accurately calculate rates. We also show method gives minimal infinite features. A sequel addresses challenge’s second on structure.