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

机译：定位潜在结构规范不确定性：隐马尔可夫模型的熵分布

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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.
机译：本文讨论了隐马尔可夫模型的状态推断。这些模型依赖于未观察到的状态，这些状态通常具有有意义的解释。这使得必须开发用于量化状态不确定性的诊断工具。解释给定隐马尔可夫链模型的观察序列的状态序列的熵可以视为状态序列不确定性的标准度量。经典的多维后验状态（或平滑化）概率分布图未反映状态序列不确定性的这种规范度量，因为这些后验概率的计算固有存在边际化。在这里，我们介绍一种具有以下特性的新型轮廓：（i）这些条件熵的轮廓是状态序列不确定性沿着序列的规范度量的分解，并可以定位该不确定性，（ii）这些轮廓是一维的，因此在树结构上仍易于解释。我们展示了如何扩展隐马尔可夫链和树模型的平滑算法，以有效地计算这些熵轮廓。序列和树数据示例说明了熵配置文件的使用。

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