| Presentation | 2015-03-05 Bayer Projection of Conditional Normalized Maximum Likelihood Distributions in Poisson Model and Linear Regression Model Mutsuki KOJIMA, Fumiyasu KOMAKI, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In the Poisson model and the linear regression model, we reveal the relations between the conditional normalized maximum likelihood (CNML) distributions and Bayesian predictive densities based on the latent information priors (LIPs). In particular, CNML3, which is one type of CNML distributions, is investigated. The Bayes projection of a predictive density is an information projection of the predictive density on a set of Bayesian predictive densities. For the Poisson model, we numerically verify that the Bayes projection of CNML3 is asymptotically identical to the Bayesian predictive density based on LIP. In addition, for the linear regression model, we prove that the Bayes projection of CNML3 coincides with the Bayesian predictive density based on LIP. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | conditional mutual information / Kullback-Leibler divergence / latent information prior / least favorable prior / minimax predictive density / regret / Renyi divergence |
| Paper # | IBISML2014-86 |
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| Conference Information | |
| Committee | IBISML |
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| Conference Date | 2015/2/26(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | 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) | Bayer Projection of Conditional Normalized Maximum Likelihood Distributions in Poisson Model and Linear Regression Model |
| Sub Title (in English) | |
| Keyword(1) | conditional mutual information |
| Keyword(2) | Kullback-Leibler divergence |
| Keyword(3) | latent information prior |
| Keyword(4) | least favorable prior |
| Keyword(5) | minimax predictive density |
| Keyword(6) | regret |
| Keyword(7) | Renyi divergence |
| 1st Author's Name | Mutsuki KOJIMA |
| 1st Author's Affiliation | Graduate School of Information Science and Technology, The University of Tokyo() |
| 2nd Author's Name | Fumiyasu KOMAKI |
| 2nd Author's Affiliation | Graduate School of Information Science and Technology, The University of Tokyo:RIKEN Brain Science Institute |
| Date | 2015-03-05 |
| Paper # | IBISML2014-86 |
| Volume (vol) | vol.114 |
| Number (no) | 502 |
| Page | pp.pp.- |
| #Pages | 7 |
| Date of Issue | |