| Presentation | 2018-03-08 Information Geometrical Study of Cluster-Model Approximation for Boltzmann Machines Kenta Toyoda, Tomohiro Ogawa, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In learning algorithms for Boltzmann machines, it is necessary but very hard to calculate the expectation of units with respect to the equilibrium states of the machines.To address this difficulty, the mean-field approximation has been used.It is known that the mean-field approximation is obtained by the $e$-projection from the original model to the mean-field sub-model in the information geometrical study [7].In this paper, we extend the information geometrical approach by introducing a cluster-model composed of clusters of units, and study the $e$-projection to the cluster-model. We give a necessary and sufficient condition for the $e$-projection and propose an alternating numerical algorithm to find the $e$-projection, which is verified by computer simulations. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Boltzmann Machines / Information Geometry / Kullback-Leibler divergence / $e$-projection |
| Paper # | IT2017-104,ISEC2017-92,WBS2017-85 |
| Date of Issue | 2018-03-01 (IT, ISEC, WBS) |
| Conference Information | |
| Committee | WBS / IT / ISEC |
|---|---|
| Conference Date | 2018/3/8(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Katsusika Campas, Tokyo University of Science |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | joint meeting of IT, ISEC, and WBS |
| Chair | Fumiaki Maehara(Waseda Univ.) / Masayoshi Ohashi(Fukuoka Univ.) / Kazuto Ogawa(NHK) |
| Vice Chair | Masanori Hamamura(Kochi Univ. of Tech.) / Fumie Ono(NICT) / Jun Muramatsu(NTT) / Atsushi Fujioka(Kanagawa Univ.) / Shiho Moriai(NICT) |
| Secretary | Masanori Hamamura(Mitsubishi Electric) / Fumie Ono(Ibaraki Univ.) / Jun Muramatsu(Yokohama College of Commerce) / Atsushi Fujioka(UEC) / Shiho Moriai(Tohoku Univ.) |
| Assistant | Akira Nakamura(Tokyo Univ. of Science) / Ryohei Nakamura(National Defense Academy) / Sigeaki Kuzuoka(wakayama univ.) / Keita Emura(NICT) / Yuichi Komano(TOSHIBA) / Yuuji Suga(IIJ) |
| Paper Information | |
| Registration To | Technical Committee on Wideband System / Technical Committee on Information Theory / Technical Committee on Information Security |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Information Geometrical Study of Cluster-Model Approximation for Boltzmann Machines |
| Sub Title (in English) | |
| Keyword(1) | Boltzmann Machines |
| Keyword(2) | Information Geometry |
| Keyword(3) | Kullback-Leibler divergence |
| Keyword(4) | $e$-projection |
| 1st Author's Name | Kenta Toyoda |
| 1st Author's Affiliation | The University of Electro-Communications(Univ. of Electro- Commu.) |
| 2nd Author's Name | Tomohiro Ogawa |
| 2nd Author's Affiliation | The University of Electro-Communications(Univ. of Electro- Commu.) |
| Date | 2018-03-08 |
| Paper # | IT2017-104,ISEC2017-92,WBS2017-85 |
| Volume (vol) | vol.117 |
| Number (no) | IT-487,ISEC-488,WBS-489 |
| Page | pp.pp.7-12(IT), pp.7-12(ISEC), pp.7-12(WBS), |
| #Pages | 6 |
| Date of Issue | 2018-03-01 (IT, ISEC, WBS) |