Stochastic complexities of hidden Markov models
Stochastic complexities of hidden Markov models
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隐马尔可夫模型的随机复杂性
DOI：
10.1109/nnsp.2003.1318017
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Sumio Watanabe
中科院分区：
文献类型：
--
作者：
Keisuke Yamazaki;Sumio Watanabe
隐马尔可夫模型现在被应用于许多领域，例如语音识别、自然语言处理等。然而，由于隐马尔可夫模型是不可识别的，因此模型分析的数学基础尚未构建。近年来，我们发展了代数几何方法，使我们能够分析非正则和不可辨识的模型。在本文中，我们将该方法应用于隐马尔可夫模型，并以数学严格的方式揭示其随机复杂性的渐近阶。
Hidden Markov models are now used in many fields, for example, speech recognition, natural language processing etc. However, the mathematical foundation of analysis for the models has not yet been constructed, since the HMMs are non-identifiable. In recent years, we have developed the algebraic geometrical method that allows us to analyze the non-regular and non-identifiable models. In this paper, we apply this method to the HMM and reveal the asymptotic order of its stochastic complexity in the mathematically rigorous way.