Inference in Hidden Markov Models with Explicit State Duration Distributions

TL;DR

This paper introduces a tuning-free, black-box inference method for Explicit-duration Hidden Markov Models (EDHMMs), enabling direct estimation of state duration distributions without approximations.

Contribution

It adapts nonparametric inference techniques to EDHMMs, allowing for flexible, parameter-free inference of state durations in a unified framework.

Findings

Developed a new inference procedure for EDHMMs

Eliminated need for truncation or approximations in duration estimation

Enhanced flexibility in modeling state durations

Abstract

In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterisation and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference.