Bayesian Nonparametric Hidden Semi-Markov Models
Matthew J. Johnson, Alan S. Willsky; 14(Feb):673−701, 2013.
AbstractThere 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-Markov modeling, which has been developed mainly in the parametric non-Bayesian 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.