Paper Abstract and Keywords |
Presentation |
2012-11-08 15:00
On Dimensionality Recovery Guarantee of Variational Bayesian PCA Shinichi Nakajima (Nikon), Ryota Tomioka (Univ. of Tokyo), Masashi Sugiyama (Tokyo Inst. of Tech.), Derin Babacan (Illinois Univ.) IBISML2012-66 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The variational Bayesian (VB) approach is
one of the best tractable approximations to the Bayesian estimation,
and it was demonstrated to perform well in many applications.
However, its good performance was not fully understood theoretically.
For example, VB sometimes produces a sparse solution,
which is regarded as a practical advantage of VB,
but such sparsity is hardly observed in the rigorous Bayesian estimation.
In this paper, we focus on probabilistic PCA and
give more theoretical insight into the empirical success of VB.
More specifically, for the situation where the noise variance is unknown,
we derive a sufficient condition for perfect recovery of the true PCA
dimensionality
in the large-scale limit
when the size of an observed matrix
goes to infinity with its column-row ratio fixed.
In our analysis, we obtain bounds for a noise variance estimator
and simple closed-form solutions for other parameters,
which themselves are actually very useful for better implementation of VB-PCA. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
matrix factorization / variational Bayes / sparsity / perfect dimensionality recovery / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 112, no. 279, IBISML2012-66, pp. 229-236, Nov. 2012. |
Paper # |
IBISML2012-66 |
Date of Issue |
2012-10-31 (IBISML) |
ISSN |
Print edition: ISSN 0913-5685 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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IBISML2012-66 |
Conference Information |
Committee |
IBISML |
Conference Date |
2012-11-07 - 2012-11-09 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Bunkyo School Building, Tokyo Campus, Tsukuba Univ. |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
the 15th Information-Based Induction Sciences Workshop |
Paper Information |
Registration To |
IBISML |
Conference Code |
2012-11-IBISML |
Language |
English (Japanese title is available) |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On Dimensionality Recovery Guarantee of Variational Bayesian PCA |
Sub Title (in English) |
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Keyword(1) |
matrix factorization |
Keyword(2) |
variational Bayes |
Keyword(3) |
sparsity |
Keyword(4) |
perfect dimensionality recovery |
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1st Author's Name |
Shinichi Nakajima |
1st Author's Affiliation |
Nikon Corporation (Nikon) |
2nd Author's Name |
Ryota Tomioka |
2nd Author's Affiliation |
The University of Tokyo (Univ. of Tokyo) |
3rd Author's Name |
Masashi Sugiyama |
3rd Author's Affiliation |
Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
4th Author's Name |
Derin Babacan |
4th Author's Affiliation |
University of Illinois (Illinois Univ.) |
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Speaker |
Author-1 |
Date Time |
2012-11-08 15:00:00 |
Presentation Time |
150 minutes |
Registration for |
IBISML |
Paper # |
IBISML2012-66 |
Volume (vol) |
vol.112 |
Number (no) |
no.279 |
Page |
pp.229-236 |
#Pages |
8 |
Date of Issue |
2012-10-31 (IBISML) |
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