Learning Hidden Markov Models to Fit Long-Term Dependencies

We propose in this report a novel approach to the induction of the structure of Hidden Markov Models (HMMs). The notion of partially observable Markov models (POMMs) is introduced. POMMs form a particular case of HMMs where any state emits a single letter with probability one, but several states can emit the same letter. It is shown that any HMM can be represented by an equivalent POMM. The proposed induction algorithm aims at finding a POMM fitting the dynamics of the target machine, that is to best approximate the stationary distribution and the mean first passage times observed in the sample. The induction relies on non-linear optimization and iterative state splitting from an initial order one Markov chain. Experimental results illustrate the advantages of the proposed approach as compared to Baum-Welch HMM estimation or back-off smoothed Ngrams equivalent to variable order Markov chains. Faculté des sciences appliquées UCL Université catholique de Louvain Learning Hidden Markov Models to Fit Long-Term Dependencies Jérôme Callut and Pierre Dupont Department of Computing Science and Engineering, INGI Université catholique de Louvain, Place Sainte-Barbe 2, B-1348 Louvain-la-Neuve, Belgium Email: {jcal,pdupont}@info.ucl.ac.be