| Presentation | 2018-03-05 Exponential Family of Markov Kernels and Asymptotic Exponential Family of Markov Sources Jun'ichi Takeuchi, Hiroshi Nagaoka, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | For parametric models of Markov sources, we prove that the notion of asymptotic exponential family is equivalent to the notion of exponential family of Markov kernels. The former was introduced by Takeuchi and Barron (1998) for families of general stochastic processes, inspired by the exponential family of Markov chains discovered by Ito and Amari (1988), while the latter was introduced by Nakagawa and Kanaya (1993) for one-dimensional families of Markov sources based on the discussion by Ito and Amari (1988) and later the general form was established by Nagaoka (2005). The discussion in this report is some refinement of works of Takeuchi and Nagaoka (2017). |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | exponential family / Markov model / information geometry |
| Paper # | IBISML2017-93 |
| Date of Issue | 2018-02-26 (IBISML) |
| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2018/3/5(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nishijin Plaza, Kyushu University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Statisitical Mathematics, Machine Learning, Data Mining, etc. |
| Chair | Kenji Fukumizu(ISM) |
| Vice Chair | Masashi Sugiyama(Univ. of Tokyo) / Hisashi Kashima(Kyoto Univ.) |
| Secretary | Masashi Sugiyama(Nagoya Inst. of Tech.) / Hisashi Kashima(Univ. of Tokyo) |
| Assistant | Tomoharu Iwata(NTT) / Toshihiro Kamishima(AIST) |
| Paper Information | |
| Registration To | Technical Committee on Infomation-Based Induction Sciences and Machine Learning |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Exponential Family of Markov Kernels and Asymptotic Exponential Family of Markov Sources |
| Sub Title (in English) | |
| Keyword(1) | exponential family |
| Keyword(2) | Markov model |
| Keyword(3) | information geometry |
| 1st Author's Name | Jun'ichi Takeuchi |
| 1st Author's Affiliation | Kyushu University(Kyushu Univ.) |
| 2nd Author's Name | Hiroshi Nagaoka |
| 2nd Author's Affiliation | The University of Electro-Communications(UEC) |
| Date | 2018-03-05 |
| Paper # | IBISML2017-93 |
| Volume (vol) | vol.117 |
| Number (no) | IBISML-475 |
| Page | pp.pp.21-25(IBISML), |
| #Pages | 5 |
| Date of Issue | 2018-02-26 (IBISML) |