Learning Complex Uncertain States Changes via Asymmetric Hidden Markov Models: an Industrial Case

Marcos L.P. Bueno, Arjen Hommersom, Peter J.F. Lucas, Sicco Verwer, Alexis Linard
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:50-61, 2016.

Abstract

In many problems involving multivariate time series, Hidden Markov Models (HMMs) are often employed to model complex behavior over time. HMMs can, however, require large number of states, that can lead to overfitting issues especially when limited data is available. In this work, we propose a family of models called Asymmetric Hidden Markov Models (HMM-As), that generalize the emission distributions to arbitrary Bayesian-network distributions. The new model allows for state-specific graphical structures defined over the space of observable features, what renders more compact state spaces and hence a better handling of the complexity-overfitting trade-off. We first define asymmetric HMMs, followed by the definition of a learning procedure inspired on the structural expectation-maximization framework allowing for decomposing learning per state. Then, we relate representation aspects of HMM-As to standard and independent HMMs. The last contribution of the paper is a set of experiments that elucidate the behavior of asymmetric HMMs on practical scenarios, including simulations and industry-based scenarios. The empirical results indicate that HMMs are limited when learning structured distributions, what is prevented by the more parsimonious representation of HMM-As. Furthermore, HMM-As showed to be promising in uncovering multiple graphical structures and providing better model fit in a case study from the domain of large-scale printers, thus providing additional problem insight.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-bueno16, title = {Learning Complex Uncertain States Changes via Asymmetric Hidden {M}arkov Models: an Industrial Case}, author = {Bueno, Marcos L.P. and Hommersom, Arjen and Lucas, Peter J.F. and Verwer, Sicco and Linard, Alexis}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {50--61}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/bueno16.pdf}, url = {https://proceedings.mlr.press/v52/bueno16.html}, abstract = {In many problems involving multivariate time series, Hidden Markov Models (HMMs) are often employed to model complex behavior over time. HMMs can, however, require large number of states, that can lead to overfitting issues especially when limited data is available. In this work, we propose a family of models called Asymmetric Hidden Markov Models (HMM-As), that generalize the emission distributions to arbitrary Bayesian-network distributions. The new model allows for state-specific graphical structures defined over the space of observable features, what renders more compact state spaces and hence a better handling of the complexity-overfitting trade-off. We first define asymmetric HMMs, followed by the definition of a learning procedure inspired on the structural expectation-maximization framework allowing for decomposing learning per state. Then, we relate representation aspects of HMM-As to standard and independent HMMs. The last contribution of the paper is a set of experiments that elucidate the behavior of asymmetric HMMs on practical scenarios, including simulations and industry-based scenarios. The empirical results indicate that HMMs are limited when learning structured distributions, what is prevented by the more parsimonious representation of HMM-As. Furthermore, HMM-As showed to be promising in uncovering multiple graphical structures and providing better model fit in a case study from the domain of large-scale printers, thus providing additional problem insight.} }
Endnote
%0 Conference Paper %T Learning Complex Uncertain States Changes via Asymmetric Hidden Markov Models: an Industrial Case %A Marcos L.P. Bueno %A Arjen Hommersom %A Peter J.F. Lucas %A Sicco Verwer %A Alexis Linard %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-bueno16 %I PMLR %P 50--61 %U https://proceedings.mlr.press/v52/bueno16.html %V 52 %X In many problems involving multivariate time series, Hidden Markov Models (HMMs) are often employed to model complex behavior over time. HMMs can, however, require large number of states, that can lead to overfitting issues especially when limited data is available. In this work, we propose a family of models called Asymmetric Hidden Markov Models (HMM-As), that generalize the emission distributions to arbitrary Bayesian-network distributions. The new model allows for state-specific graphical structures defined over the space of observable features, what renders more compact state spaces and hence a better handling of the complexity-overfitting trade-off. We first define asymmetric HMMs, followed by the definition of a learning procedure inspired on the structural expectation-maximization framework allowing for decomposing learning per state. Then, we relate representation aspects of HMM-As to standard and independent HMMs. The last contribution of the paper is a set of experiments that elucidate the behavior of asymmetric HMMs on practical scenarios, including simulations and industry-based scenarios. The empirical results indicate that HMMs are limited when learning structured distributions, what is prevented by the more parsimonious representation of HMM-As. Furthermore, HMM-As showed to be promising in uncovering multiple graphical structures and providing better model fit in a case study from the domain of large-scale printers, thus providing additional problem insight.
RIS
TY - CPAPER TI - Learning Complex Uncertain States Changes via Asymmetric Hidden Markov Models: an Industrial Case AU - Marcos L.P. Bueno AU - Arjen Hommersom AU - Peter J.F. Lucas AU - Sicco Verwer AU - Alexis Linard BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-bueno16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 50 EP - 61 L1 - http://proceedings.mlr.press/v52/bueno16.pdf UR - https://proceedings.mlr.press/v52/bueno16.html AB - In many problems involving multivariate time series, Hidden Markov Models (HMMs) are often employed to model complex behavior over time. HMMs can, however, require large number of states, that can lead to overfitting issues especially when limited data is available. In this work, we propose a family of models called Asymmetric Hidden Markov Models (HMM-As), that generalize the emission distributions to arbitrary Bayesian-network distributions. The new model allows for state-specific graphical structures defined over the space of observable features, what renders more compact state spaces and hence a better handling of the complexity-overfitting trade-off. We first define asymmetric HMMs, followed by the definition of a learning procedure inspired on the structural expectation-maximization framework allowing for decomposing learning per state. Then, we relate representation aspects of HMM-As to standard and independent HMMs. The last contribution of the paper is a set of experiments that elucidate the behavior of asymmetric HMMs on practical scenarios, including simulations and industry-based scenarios. The empirical results indicate that HMMs are limited when learning structured distributions, what is prevented by the more parsimonious representation of HMM-As. Furthermore, HMM-As showed to be promising in uncovering multiple graphical structures and providing better model fit in a case study from the domain of large-scale printers, thus providing additional problem insight. ER -
APA
Bueno, M.L., Hommersom, A., Lucas, P.J., Verwer, S. & Linard, A.. (2016). Learning Complex Uncertain States Changes via Asymmetric Hidden Markov Models: an Industrial Case. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:50-61 Available from https://proceedings.mlr.press/v52/bueno16.html.

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