Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models

Jean-Baptiste Durand 1 Yann Guédon 2, 3
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 report 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 multivariate state profiles computed by the smoothing algorithm, which summarizes the possible state sequences. Here, we introduce a new type of profiles which 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 localize this uncertainty, (ii) these profiles are univariate 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.
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Submitted on : Wednesday, February 29, 2012 - 2:23:04 PM
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  • HAL Id : hal-00675223, version 1
  • ARXIV : 1202.6545

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Jean-Baptiste Durand, Yann Guédon. Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models. [Research Report] RR-7896, Inria. 2012, pp.43. ⟨hal-00675223⟩

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