Identifying combinatorially symmetric Hidden Markov Models

TL;DR

This paper introduces a criterion for uniquely identifying parameters of combinatorially symmetric Hidden Markov Models using graph structure, enabling explicit reconstruction when observed states form a zero forcing set.

Contribution

It provides a sufficient condition for unique parameter identification based on the transition matrix structure and zero forcing sets, along with an explicit reconstruction method.

Findings

Unique identifiability criterion established

Explicit reconstruction method provided

Applicable when observed states form a zero forcing set

Abstract

We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of the graph of the Markov model then it is uniquely identifiable and an explicit reconstruction method is given.