The Hierarchical Dirichlet Process Hidden Semi-Markov Model

Matthew Johnson, Alan Willsky
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:260-267, 2010.

Abstract

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. 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 in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-johnson10a, title = {The Hierarchical {D}irichlet Process Hidden Semi-{M}arkov Model}, author = {Johnson, Matthew and Willsky, Alan}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {260--267}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/johnson10a/johnson10a.pdf}, url = {https://proceedings.mlr.press/r8/johnson10a.html}, abstract = {There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. 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 in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T The Hierarchical Dirichlet Process Hidden Semi-Markov Model %A Matthew Johnson %A Alan Willsky %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-johnson10a %I PMLR %P 260--267 %U https://proceedings.mlr.press/r8/johnson10a.html %V R8 %X There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. 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 in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code. %Z Reissued by PMLR on 04 October 2026.
APA
Johnson, M. & Willsky, A.. (2010). The Hierarchical Dirichlet Process Hidden Semi-Markov Model. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:260-267 Available from https://proceedings.mlr.press/r8/johnson10a.html. Reissued by PMLR on 04 October 2026.

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