Paper Abstract and Keywords |
Presentation |
2020-07-16 14:45
Asymptotic Evaluation of $alpha$-divergence between VB Posterior Predictive Distribution and Bayesian Predictive Distribution Kazuki Yamada, Shota Saito, Toshiyasu Matsushima (Waseda Univ.) IT2020-14 |
Abstract |
(in Japanese) |
(See Japanese page) |
(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) |
(in English) |
Asymptotic Analysis / $alpha$ divergence / Bayesian Predictive Distribution / Variational Bayes / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 120, no. 105, IT2020-14, pp. 19-23, July 2020. |
Paper # |
IT2020-14 |
Date of Issue |
2020-07-09 (IT) |
ISSN |
Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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IT2020-14 |
Conference Information |
Committee |
IT |
Conference Date |
2020-07-16 - 2020-07-16 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Online |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
Freshman session, General |
Paper Information |
Registration To |
IT |
Conference Code |
2020-07-IT |
Language |
Japanese |
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) |
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Keyword(1) |
Asymptotic Analysis |
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$alpha$ divergence |
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Bayesian Predictive Distribution |
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Variational Bayes |
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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 |
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Waseda University (Waseda Univ.) |
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Speaker |
Author-1 |
Date Time |
2020-07-16 14:45:00 |
Presentation Time |
25 minutes |
Registration for |
IT |
Paper # |
IT2020-14 |
Volume (vol) |
vol.120 |
Number (no) |
no.105 |
Page |
pp.19-23 |
#Pages |
5 |
Date of Issue |
2020-07-09 (IT) |
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