Information geometry of the family of Markov kernels defined by a context tree
Information geometry of the family of Markov kernels defined by a context tree
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由上下文树定义的马尔可夫核族的信息几何
DOI：
10.1109/itw.2017.8278008
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
H. Nagaoka
中科院分区：
文献类型：
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作者：
J. Takeuchi;H. Nagaoka
我们证明了树模型是马尔可夫核的指数族（e族），当且仅当它是FSMX模型。马尔可夫核的e族的概念首先由Nakagawa和Kanaya（'93）在一维情况下引入。然后，Nagaoka（'05）给出了它的建立形式，Hayashi & Watanabe（' 16）讨论了它。树模型是由上下文树定义的马尔可夫模型。Weinberger等人指出，（'95）树模型被分为两类; FSMX模型和非FSMX模型，这取决于它们的上下文树的形状。FSMX模型是一个树模型和有限状态机。我们进一步证明了，对于马尔可夫模型，马尔可夫核的e族等价于Takeuchi &巴伦（'98）引入的渐近e族。注意，Takeuchi & Kawabata（'07）证明了非FSMX树模型对于二进制字母表的情况不是渐近e族。本文改进了他们的结果，揭示了树模型的信息几何性质。
We prove that a tree model is an exponential family (e-family) of Markov kernels, if and only if it is an FSMX model. The notion of e-family of Markov kernels was first introduced by Nakagawa and Kanaya ('93) in the one-dimensional case. Then, Nagaoka ('05) gave its established form, and Hayashi & Watanabe ('16) discussed it. A tree model is the Markov model defined by a context tree. It is noted by Weinberger et al., ('95) that tree models are classified into two classes; FSMX models and non-FSMX models, depending on the shape of their context trees. The FSMX model is a tree model and a finite state machine. We further show that, for Markov models, the e-family of Markov kernels is equivalent to the asymptotic e-family, which was introduced by Takeuchi & Barron ('98). Note that Takeuchi & Kawabata ('07) proved that non-FSMX tree models are not asymptotic e-families for the binary alphabet case. This paper enhances their result and reveals the information geometrical properties of tree models.
马尔可夫源的 Jeffreys 混合物的性质
DOI：
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发表时间：
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期刊：
IEEE Transactions on Information Theory, accepted for publication
影响因子：
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作者：
J-I. Takeuchi;A. Barron;T. Kawabata
通讯作者：
T. Kawabata
DOI：
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发表时间：
2005
期刊：
第28回情報理論とその応用シンポジウム予稿集
影响因子：
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作者：
Doi;T.;Fujito;T.;H.Ishihara;H.Nagaoka
通讯作者：
H.Nagaoka