Bayesian Nonparametric Hidden Semi-Markov Models

TL;DR

This paper introduces the HDP-HSMM, a Bayesian nonparametric model that extends HDP-HMMs to explicitly model state durations, enabling more interpretable analysis of sequential data with non-geometric durations.

Contribution

We develop the HDP-HSMM, a novel Bayesian nonparametric semi-Markov model with efficient sampling algorithms, expanding inference tools for hierarchical Bayesian models.

Findings

Demonstrated the model's effectiveness on synthetic data.

Applied the model successfully to real-world sequential data.

Provided scalable inference algorithms for complex hierarchical models.

Abstract

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments.