Quantifying and localizing state uncertainty in hidden Markov models using conditional entropy profiles

Jean-Baptiste Durand; Yann Guédon

Quantifying and localizing state uncertainty in hidden Markov models using conditional entropy profiles

Jean-Baptiste Durand ^{1, 2} 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

3 UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales

Abstract : Abstract. A family of graphical hidden Markov models that generalizes hidden Markov chain (HMC) and tree (HMT) models is introduced. It is shown that global uncertainty on the state process can be decomposed as a sum of conditional entropies that are interpreted as local contributions to global uncertainty. An efficient algorithm is derived to compute conditional entropy profiles in the case of HMC and HMT models. The relevance of these profiles and their complementarity with other state restoration algorithms for interpretation and diagnosis of hidden states is highlighted. It is also shown that classical smoothing profiles (posterior marginal probabilities of the states at each time, given the observations) cannot be related to global state uncertainty in the general case.

keyword : Hidden Markov models State inference Conditional entropy

Document type :

Conference papers

Domain :

Mathematics [math] / Statistics [math.ST]

Statistics [stat] / Statistics Theory [stat.TH]

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https://hal.inria.fr/hal-01058278
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Submitted on : Tuesday, August 26, 2014 - 2:39:26 PM
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Quantifying and localizing state uncertainty in hidden Markov models using conditional entropy profiles

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