Algebraic geometry and stochastic complexity of hidden Markov models
Algebraic geometry and stochastic complexity of hidden Markov models
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DOI：
10.1016/j.neucom.2005.02.014
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发表时间：
2005-12-01
期刊：
影响因子：
6
通讯作者：
Watanabe, S
中科院分区：
文献类型：
--
作者：
Yamazaki, K;Watanabe, S
隐马尔可夫模型在语音识别、自然语言处理等领域有着广泛的应用，但由于隐马尔可夫模型的不可识别性，使得其分析的数学基础尚未建立，近年来，我们发展了代数几何方法，使我们能够分析非正则、不可识别的模型。本文将该方法应用于隐马尔可夫模型，从数学上严格地揭示了隐马尔可夫模型的渐近随机复杂性，结果表明贝叶斯估计使得推广误差很小，而众所周知的BIC与随机复杂性是不同的。(c)2005 Elsevier B.V.保留所有权利。
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 is not yet constructed, since the HMM is 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 stochastic complexity in a mathematically rigorous way.Our results show that the Bayesian estimation makes the generalization error small and that the well known BIC is different from the stochastic complexity. (c) 2005 Elsevier B.V. All rights reserved.