Information geometry of the family of Markov kernels defined by a context tree

Jun'Ichi Takeuchi, Hiroshi Nagaoka

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

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.

本文言語英語
ホスト出版物のタイトル2017 IEEE Information Theory Workshop, ITW 2017
出版社Institute of Electrical and Electronics Engineers Inc.
ページ429-433
ページ数5
ISBN(電子版)9781509030972
DOI
出版ステータス出版済み - 1 31 2018
イベント2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, 台湾省、中華民国
継続期間: 11 6 201711 10 2017

出版物シリーズ

名前IEEE International Symposium on Information Theory - Proceedings
2018-January
ISSN(印刷版)2157-8095

その他

その他2017 IEEE Information Theory Workshop, ITW 2017
Country台湾省、中華民国
CityKaohsiung
Period11/6/1711/10/17

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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