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Localizing the latent structure canonical uncertainty: entropy profiles for hidden Markov models

Jean-Baptiste Durand 1, 2 Yann Guédon 3, 2 
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
2 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
Abstract : This paper addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state uncertainty. The entropy of the state sequence that explains an observed sequence for a given hidden Markov chain model can be considered as the canonical measure of state sequence uncertainty. This canonical measure of state sequence uncertainty is not reflected by the classic multidimensional posterior state (or smoothed) probability profiles because of the marginalization that is intrinsic in the computation of these posterior probabilities. Here, we introduce a new type of profiles that have the following properties: (i) these profiles of conditional entropies are a decomposition of the canonical measure of state sequence uncertainty along the sequence and makes it possible to localise this uncertainty, (ii) these profiles are unidimensional and thus remain easily interpretable on tree structures. We show how to extend the smoothing algorithms for hidden Markov chain and tree models to compute these entropy profiles efficiently. The use of entropy profiles is illustrated by sequence and tree data examples.
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Submitted on : Wednesday, January 7, 2015 - 10:44:31 AM
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Jean-Baptiste Durand, Yann Guédon. Localizing the latent structure canonical uncertainty: entropy profiles for hidden Markov models. Statistics and Computing, 2016, 26 (1), pp.549-567. ⟨10.1007/s11222-014-9494-9⟩. ⟨hal-01090836⟩



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