| Presentation | 2020-07-16 Asymptotic Evaluation of $alpha$-divergence between VB Posterior Predictive Distribution and Bayesian Predictive Distribution Kazuki Yamada, Shota Saito, Toshiyasu Matsushima, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In this paper, we consider the problem of determining probability distribution of $X_{n+1}$ given ${X_i }_{i=1}^{n}$ following i.i.d. distribution. We assume log loss on probability distribution of $X_{n+1}$ and derive Bayesian predictive distribution under Bayes criteria. When parametric model contains latent variables, it is difficult to obtain posterior distribution appearing in Bayesian predictive distribution analytically. In this situation, we constitute a new predictive distribution substituting posterior distribution to VB posterior derived by variational bayes. We need to verify how close new predictive distribution to Bayesian predictive distribution. Previous research shows that total variation between Bayesian predictive distribution and VB posterior predictive distribution converges to 0 in probability under some assumptions. We show that $alpha$-divergence between two predictive distributions also converges to 0 in probability. Also, previous research is naturally derived by our result by using Pinsker's inequality. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Asymptotic Analysis / $alpha$ divergence / Bayesian Predictive Distribution / Variational Bayes |
| Paper # | IT2020-14 |
| Date of Issue | 2020-07-09 (IT) |
| Conference Information | |
| Committee | IT |
|---|---|
| Conference Date | 2020/7/16(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Freshman session, General |
| Chair | Tadashi Wadayama(Nagoya Inst. of Tech.) |
| Vice Chair | Tetsuya Kojima(Tokyo Kosen) |
| Secretary | Tetsuya Kojima(Yamaguchi Univ.) |
| Assistant | Takahiro Ohta(Senshu Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Information Theory |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Asymptotic Evaluation of $alpha$-divergence between VB Posterior Predictive Distribution and Bayesian Predictive Distribution |
| Sub Title (in English) | |
| Keyword(1) | Asymptotic Analysis |
| Keyword(2) | $alpha$ divergence |
| Keyword(3) | Bayesian Predictive Distribution |
| Keyword(4) | Variational Bayes |
| 1st Author's Name | Kazuki Yamada |
| 1st Author's Affiliation | Waseda University(Waseda Univ.) |
| 2nd Author's Name | Shota Saito |
| 2nd Author's Affiliation | Waseda University(Waseda Univ.) |
| 3rd Author's Name | Toshiyasu Matsushima |
| 3rd Author's Affiliation | Waseda University(Waseda Univ.) |
| Date | 2020-07-16 |
| Paper # | IT2020-14 |
| Volume (vol) | vol.120 |
| Number (no) | IT-105 |
| Page | pp.pp.19-23(IT), |
| #Pages | 5 |
| Date of Issue | 2020-07-09 (IT) |