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

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• 作者：Jean-Baptiste Durand ; Yann Guédon
• 关键词：Conditional entropy ; Hidden Markov chain model ; Hidden Markov tree model ; Plant structure analysis
• 刊名：Statistics and Computing
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1-2
• 页码：549-567
• 全文大小：1,558 KB
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• 作者单位：Jean-Baptiste Durand (1)
  Yann Guédon (2)
  
  1. Laboratoire Jean Kuntzmann and Inria, Mistis, Univ. Grenoble Alpes, 51 Rue des Mathématiques, B.P. 53, 38041, Grenoble Cedex 9, France
  2. CIRAD, UMR AGAP and Inria, Virtual Plants, 34095, Montpellier, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375

文摘

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. Keywords Conditional entropy Hidden Markov chain model Hidden Markov tree model Plant structure analysis