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.
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 language | English |
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Title of host publication | Proceedings of the Eighth International Conference on Probabilistic Graphical Models |
Subtitle of host publication | The JMLR Workshop and Conference PGM 2016 |
Editors | A. Antonucci, G. Corani, C.P. de Campos |
Publisher | JMLR |
Pages | 50-61 |
Number of pages | 12 |
Volume | 52 |
Publication status | Published - 2016 |
Event | The Eighth International Conference on Probabilistic Graphical Models PGM 2016: JMLR - Lugano, Switzerland Duration: 6 Sept 2016 → 9 Sept 2016 |
Publication series
Name | JMLR: Workshop and Conference Proceedings |
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ISSN (Electronic) | 1938-7228 |
Conference
Conference | The Eighth International Conference on Probabilistic Graphical Models PGM 2016 |
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Country/Territory | Switzerland |
City | Lugano |
Period | 6/09/16 → 9/09/16 |
Keywords
- Probabilistic graphical models
- multivariate time series
- hidden Markov models
- asymmetric independence
- industrial processes