| Presentation | 2013-09-02 Escort distribution and Expectation Masaru TANAKA, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | A new formulation of information geometry is given by extending a translation operation on an affine space of probability density functions with up to scale from a logarithmic function to a τ- logarithmic function. In this formulation, aτ-affine space P^^～^<(τ=s)> and itsτ-affine conjugated space P^^～_#^<(τ=s)⊂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=s),a contraction is defined by integrating f(x)g(x) about random variable x, where f(x) ∈P P^^～^<(τ=s) and g(x)∈P^^～_#^<(τ=s). With a renormalization technique for aτ-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 renormalizedτ-log-likelihood. Therefore, the escort distribution is no longer necessary for us. What we need is the normalized and renormalizedτ-log-likelihood. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | τ-affine structure / τ-affine conjugate / contraction / τ-log-likelihood / escort distribution / renormalized τ-log-likelihood |
| Paper # | PRMU2013-38,IBISML2013-18 |
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| Conference Information | |
| Committee | PRMU |
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| Conference Date | 2013/8/26(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) | Escort distribution and Expectation |
| Sub Title (in English) | |
| Keyword(1) | τ-affine structure |
| Keyword(2) | τ-affine conjugate |
| Keyword(3) | contraction |
| Keyword(4) | τ-log-likelihood |
| Keyword(5) | escort distribution |
| Keyword(6) | renormalized τ-log-likelihood |
| 1st Author's Name | Masaru TANAKA |
| 1st Author's Affiliation | Faculty of Science, Fukuoka University() |
| Date | 2013-09-02 |
| Paper # | PRMU2013-38,IBISML2013-18 |
| Volume (vol) | vol.113 |
| Number (no) | 196 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |