Learning Partially Observable Markov Models from First Passage Times

Authors:
Jérôme Callut;Pierre Dupont
Affiliations:
Department of Computing Science and Engineering, INGI, Université catholique de Louvain, Place Sainte-Barbe 2, B-1348 Louvain-la-Neuve, Belgium and UCL Machine Learning Group,;Department of Computing Science and Engineering, INGI, Université catholique de Louvain, Place Sainte-Barbe 2, B-1348 Louvain-la-Neuve, Belgium and UCL Machine Learning Group,
Venue:
ECML '07 Proceedings of the 18th European conference on Machine Learning
Year:
2007

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Abstract

We propose a novel approach to learn the structure of Partially Observable Markov Models (POMMs) and to estimate jointly their parameters. POMMs are graphical models equivalent to Hidden Markov Models (HMMs). The model structure is built to support the First Passage Times (FPT) dynamics observed in the training sample. We argue that the FPT in POMMs are closely related to the model structure. Starting from a standard Markov chain, states are iteratively added to the model. A novel algorithm POMMPHit is proposed to estimate the POMM transition probabilities to fit the sample FPT dynamics. The transitions with the lowest expected passage times are trimmed off from the model. Practical evaluations on artificially generated data and on DNA sequence modeling show the benefits over Bayesian model induction or EM estimation of ergodic models with transition trimming.