Learning Parametric-Output HMMs with Two Aliased States

Roi Weiss, Boaz Nadler
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:635-644, 2015.

Abstract

In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-weiss15, title = {Learning Parametric-Output HMMs with Two Aliased States}, author = {Weiss, Roi and Nadler, Boaz}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {635--644}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/weiss15.pdf}, url = {https://proceedings.mlr.press/v37/weiss15.html}, abstract = {In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.} }
Endnote
%0 Conference Paper %T Learning Parametric-Output HMMs with Two Aliased States %A Roi Weiss %A Boaz Nadler %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-weiss15 %I PMLR %P 635--644 %U https://proceedings.mlr.press/v37/weiss15.html %V 37 %X In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.
RIS
TY - CPAPER TI - Learning Parametric-Output HMMs with Two Aliased States AU - Roi Weiss AU - Boaz Nadler BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-weiss15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 635 EP - 644 L1 - http://proceedings.mlr.press/v37/weiss15.pdf UR - https://proceedings.mlr.press/v37/weiss15.html AB - In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations. ER -
APA
Weiss, R. & Nadler, B.. (2015). Learning Parametric-Output HMMs with Two Aliased States. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:635-644 Available from https://proceedings.mlr.press/v37/weiss15.html.

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