Hidden Markov Models with mixtures as emission distributions

TL;DR

This paper introduces a flexible semiparametric Hidden Markov Model with mixture emissions, adapting the EM algorithm for parameter inference, and proposes hierarchical initialization and model selection criteria, demonstrated through simulations and biological data.

Contribution

It presents a novel semiparametric HMM with mixture emissions, including a hierarchical initialization method and BIC-like criteria for model selection.

Findings

Effective in simulation studies for classification accuracy

Hierarchical merging improves model interpretability

Applicable to biological datasets with promising results

Abstract

In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the classical EM algorithm can be adapted to infer the model parameters. For the initialisation step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the merging criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN.