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Inference in finite state space non parametric Hidden Markov Models and applications

机译：有限状态空间非参数隐马尔可夫模型的推论与应用

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摘要

Hidden Markov models (HMMs) are intensively used in various fields to model and classify data observed along a line (e.g. time). The fit of such models strongly relies on the choice of emission distributions that are most often chosen among some parametric family. In this paper, we prove that finite state space non parametric HMMs are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions are linearly independent. This general result allows the use of semi-or non-parametric emission distributions. Based on this result we present a series of classification problems that can be tackled out of the strict parametric framework. We derive the corresponding inference algorithms. We also illustrate their use on few biological examples, showing that they may improve the classification performances.
机译：隐马尔可夫模型（HMM）在各个领域都得到了广泛使用，以对沿一条线（例如时间）观察到的数据进行建模和分类。这种模型的拟合强烈依赖于在某些参数族中最经常选择的排放分布的选择。在本文中，我们证明，只要潜在马尔可夫链的转移矩阵具有完整秩并且发射概率分布是线性独立的，就可以识别出有限状态空间非参数HMM。该一般结果允许使用半参数或非参数发射分布。基于此结果，我们提出了一系列可以从严格的参数框架中解决的分类问题。我们推导了相应的推理算法。我们还说明了它们在几个生物学实例上的用法，表明它们可以改善分类性能。

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