| Presentation | 2014-11-18 Gauge Theory on Measure Space : τ-Information Geometry 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, this extended translation is called a τ-affine structure and an affine space with a τ-affine structure is called a τ-affine space. Its dual space is defined by taking a Holder conjugation. A contraction operation is defined on a τ-affine space and its conjugated space. This leads to Fisher metric for score functions. Then it is revealed that Fisher metric is independent of a τ-affine structure. The definition of an entropy requires a renormalization process. With a renormalization technique for a τ-log-likelihood, the contraction leads to a new definition of an expectation. This new expectation 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. By using this new expectation, a conformal entropy is also given. The conformal entropy is related to Tsallis entropy with a simple modification and gives two types of non-additivity according to formulae of τ-logarithmic function for multiplication. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | τ-affine structure / contraction / τ-log-likelihood / escort distribution / renormalization / entropy / non-additivity |
| Paper # | IBISML2014-72 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2014/11/10(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Information-Based Induction Sciences and Machine Learning (IBISML) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Gauge Theory on Measure Space : τ-Information Geometry |
| Sub Title (in English) | |
| Keyword(1) | τ-affine structure |
| Keyword(2) | contraction |
| Keyword(3) | τ-log-likelihood |
| Keyword(4) | escort distribution |
| Keyword(5) | renormalization |
| Keyword(6) | entropy |
| Keyword(7) | non-additivity |
| 1st Author's Name | Masaru TANAKA |
| 1st Author's Affiliation | Faculty of Science, Fukuoka University() |
| Date | 2014-11-18 |
| Paper # | IBISML2014-72 |
| Volume (vol) | vol.114 |
| Number (no) | 306 |
| Page | pp.pp.- |
| #Pages | 8 |
| Date of Issue | |