Products of Hidden Markov Models: It Takes N>1 to Tango

Graham Taylor, Geoffrey Hinton
Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, PMLR R7:530-537, 2009.

Abstract

Products of Hidden Markov Models (PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This may be in part due to their more computationally expensive gradient-based learning algorithm, and the intractability of computing the log likelihood of sequences under the model. In this paper, we demonstrate how the partition function can be estimated reliably via Annealed Importance Sampling. We perform experiments using contrastive di- vergence learning on rainfall data and data captured from pairs of people dancing. Our results suggest that advances in learning and evaluation for undirected graphical models and recent increases in available computing power make PoHMMs worth considering for complex time-series modeling tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR7-taylor09a, title = {Products of Hidden {M}arkov Models: It Takes N>1 to Tango}, author = {Taylor, Graham and Hinton, Geoffrey}, booktitle = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence}, pages = {530--537}, year = {2009}, editor = {Bilmes, Jeff and Ng, Andrew Y.}, volume = {R7}, series = {Proceedings of Machine Learning Research}, month = {18--21 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r7/main/assets/taylor09a/taylor09a.pdf}, url = {https://proceedings.mlr.press/r7/taylor09a.html}, abstract = {Products of Hidden Markov Models (PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This may be in part due to their more computationally expensive gradient-based learning algorithm, and the intractability of computing the log likelihood of sequences under the model. In this paper, we demonstrate how the partition function can be estimated reliably via Annealed Importance Sampling. We perform experiments using contrastive di- vergence learning on rainfall data and data captured from pairs of people dancing. Our results suggest that advances in learning and evaluation for undirected graphical models and recent increases in available computing power make PoHMMs worth considering for complex time-series modeling tasks.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Products of Hidden Markov Models: It Takes N>1 to Tango %A Graham Taylor %A Geoffrey Hinton %B Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2009 %E Jeff Bilmes %E Andrew Y. Ng %F pmlr-vR7-taylor09a %I PMLR %P 530--537 %U https://proceedings.mlr.press/r7/taylor09a.html %V R7 %X Products of Hidden Markov Models (PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This may be in part due to their more computationally expensive gradient-based learning algorithm, and the intractability of computing the log likelihood of sequences under the model. In this paper, we demonstrate how the partition function can be estimated reliably via Annealed Importance Sampling. We perform experiments using contrastive di- vergence learning on rainfall data and data captured from pairs of people dancing. Our results suggest that advances in learning and evaluation for undirected graphical models and recent increases in available computing power make PoHMMs worth considering for complex time-series modeling tasks. %Z Reissued by PMLR on 04 October 2026.
APA
Taylor, G. & Hinton, G.. (2009). Products of Hidden Markov Models: It Takes N>1 to Tango. Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R7:530-537 Available from https://proceedings.mlr.press/r7/taylor09a.html. Reissued by PMLR on 04 October 2026.

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