Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization

作者: Yoshiyuki Kabashima , Florent Krzakala , Marc Mezard , Ayaka Sakata , Lenka Zdeborova

DOI: 10.1109/TIT.2016.2556702

关键词:

摘要: … the measurements Y. In this paper we will treat this problem in the framework of Bayesian … we consider the rank to be a finite fraction of the total dimension, whereas most of existing …

参考文章(78)
Rémi Gribonval, Rodolphe Jenatton, Francis R. Bach, Local stability and robustness of sparse dictionary learning in the presence of noise arXiv: Machine Learning. pp. 41- ,(2012)
David J. Aldous, The ζ (2) limit in the random assignment problem Random Structures and Algorithms. ,vol. 18, pp. 381- 418 ,(2001) , 10.1002/RSA.1015
Jason T. Parker, Philip Schniter, Volkan Cevher, Bilinear Generalized Approximate Message Passing—Part I: Derivation IEEE Transactions on Signal Processing. ,vol. 62, pp. 5839- 5853 ,(2014) , 10.1109/TSP.2014.2357776
Marc Mézard, Giorgio Parisi, Riccardo Zecchina, Analytic and Algorithmic Solution of Random Satisfiability Problems Science. ,vol. 297, pp. 812- 815 ,(2002) , 10.1126/SCIENCE.1073287
Tom Richardson, Ruediger Urbanke, Modern Coding Theory Cambridge University Press. ,(2008) , 10.1017/CBO9780511791338
Jeremy Vila, Philip Schniter, Sundeep Rangan, Florent Krzakala, Lenka Zdeborova, Adaptive damping and mean removal for the generalized approximate message passing algorithm 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 2021- 2025 ,(2015) , 10.1109/ICASSP.2015.7178325
Rémi Gribonval, Sylvain Lesage, A survey of Sparse Component Analysis for blind source separation: principles, perspectives, and new challenges the european symposium on artificial neural networks. pp. 323- 330 ,(2006)
Montanari Andrea, Estimating random variables from random sparse observations European Transactions on Telecommunications. ,vol. 19, pp. 385- 403 ,(2008) , 10.1002/ETT.1289
Animashree Anandkumar, Praneeth Netrapalli, Alekh Agarwal, A Clustering Approach to Learn Sparsely-Used Overcomplete Dictionaries arXiv: Machine Learning. ,(2013)