Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization

We analyze the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications, such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separat...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 62; no. 7; pp. 4228 - 4265
Main Authors:	Kabashima, Yoshiyuki, Krzakala, Florent, Mezard, Marc, Sakata, Ayaka, Zdeborova, Lenka
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.07.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithm design and analysis Algorithms Bayesian analysis Complexity theory Computation Factorization Inference Matrix Noise measurement Optimization Phase transitions Prediction algorithms Principal component analysis Probability distribution Samples Sparse matrices Statistical analysis Statistical mechanics Statistical methods statistical and computational tradeoff statistical physics message passing algorithms phase transitions computational barriers Statistical inference probabilistic matrix factorization dictionary learning sparse coding
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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