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

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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.
Original languageEnglish
Title of host publicationConference on Probabilistic Graphical Models, 6-9 September 2016, Lugano, Switzerland
EditorsAlessandro Antonucci, Giorgio Corani, Cassio Polpo Campos
PublisherMLResearchPress
Pages50–61
Publication statusPublished - 2016
Externally publishedYes
Event8th International Conference on Probabilistic Graphical Models, PGM 2016 - Lugano, Switzerland
Duration: 6 Sept 20169 Sept 2016
Conference number: 8

Publication series

NameProceedings of Machine Learning Research (PMLR)
PublisherJMLR
Volume52
ISSN (Electronic)2640-3498

Conference

Conference8th International Conference on Probabilistic Graphical Models, PGM 2016
Abbreviated titlePGM
Country/TerritorySwitzerland
CityLugano
Period6/09/169/09/16

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