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 Hierarchi- cal Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonpara- metric 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 ex- tend the HDP-HMM to capture such struc- ture 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 explicit- duration 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 meth- ods on synthetic data as well as experiments on a speaker diarization problem and an ex- ample 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 Hierarchi- cal Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonpara- metric 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 ex- tend the HDP-HMM to capture such struc- ture 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 explicit- duration 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 meth- ods on synthetic data as well as experiments on a speaker diarization problem and an ex- ample 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 Hierarchi- cal Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonpara- metric 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 ex- tend the HDP-HMM to capture such struc- ture 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 explicit- duration 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 meth- ods on synthetic data as well as experiments on a speaker diarization problem and an ex- ample 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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