| Presentation | 2014-02-13 τ-information geometry : translation on a space of measurable functions Masaru TANAKA, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | τ-information geometry, that is a new formulation of information geometry, is given by extending a translation operation on an affine space consisting of measurable functions with up to scale. In this formulation, a τ-affine space P^～(τ=s) and its τ-affine conjugate space P^～(τ=1-s) play important roles, τ-affine conjugation of a point in P^～(τ=s) gives a point in P^～(τ=1-s) with the same affine coordinates. On the P^～(τ=s) × P^～(τ=1-s), a contraction, that is an inner product in some sense, is denned. With a renormalization technique for a τ-log-likelihood, the contraction leads to a new definition of an expectation. This new expectation admits a usual interpretation, but is essentially different from the usual one. It reveals that an escort distribution is nothing but a normalized and renormalized τ-log-likelihood. Therefore, the escort distribution is no longer necessary for us. What we need is the normalized and renormalized τ-log-likelihood. It is also given what αparameter in α-dual connections is. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | τ-affine structure / τ-affine conjugate / contraction / τ-log-likelihood / renormalized τ-log-likelihood / Fisher metric |
| Paper # | PRMU2013-133,CNR2013-41 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 2014/2/6(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Pattern Recognition and Media Understanding (PRMU) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | τ-information geometry : translation on a space of measurable functions |
| Sub Title (in English) | |
| Keyword(1) | τ-affine structure |
| Keyword(2) | τ-affine conjugate |
| Keyword(3) | contraction |
| Keyword(4) | τ-log-likelihood |
| Keyword(5) | renormalized τ-log-likelihood |
| Keyword(6) | Fisher metric |
| 1st Author's Name | Masaru TANAKA |
| 1st Author's Affiliation | Faculty of Science, Fukuoka University() |
| Date | 2014-02-13 |
| Paper # | PRMU2013-133,CNR2013-41 |
| Volume (vol) | vol.113 |
| Number (no) | 431 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |