Learning Parametric-Output HMMs with Two Aliased States

TL;DR

This paper addresses the challenges of learning hidden Markov models with exactly two aliased states and parametric outputs, providing theoretical characterizations and efficient algorithms for detection and learning.

Contribution

It offers a complete characterization of minimality and identifiability for two-aliased parametric-output HMMs, along with efficient algorithms for detection and parameter estimation.

Findings

Complete characterization of minimality and identifiability.

Efficient algorithms for aliasing detection and parameter learning.

Validation through simulations demonstrating effectiveness.

Abstract

In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.