Context Tree Estimation in Variable Length Hidden Markov Models

TL;DR

This paper introduces a new method for estimating the context tree in variable length hidden Markov models without prior depth bounds, proving its strong consistency and demonstrating its effectiveness through simulations.

Contribution

It presents a novel, consistent estimator for the context tree in variable length HMMs that does not require pre-specified depth limits.

Findings

Estimator is strongly consistent

Algorithm efficiently computes the estimator

Simulation studies validate the approach

Abstract

We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exponents in hidden Markov model order estimation(2003)). We propose an algorithm to efficiently compute the estimator and provide simulation studies to support our result.