The Spiked Matrix Model With Generative Priors
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Florent Krzakala | Lenka Zdeborová | Bruno Loureiro | Benjamin Aubin | Antoine Maillard | F. Krzakala | L. Zdeborová | A. Maillard | Benjamin Aubin | Bruno Loureiro | Antoine Maillard | Florent Krzakala
[1] Shlomo Shamai,et al. Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.
[2] R. Tibshirani,et al. Sparse Principal Component Analysis , 2006 .
[3] J. W. Silverstein,et al. On the empirical distribution of eigenvalues of a class of large dimensional random matrices , 1995 .
[4] Florent Krzakala,et al. Statistical and computational phase transitions in spiked tensor estimation , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).
[5] V. Marčenko,et al. DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .
[6] 西森 秀稔. Statistical physics of spin glasses and information processing : an introduction , 2001 .
[7] M. Wainwright,et al. High-dimensional analysis of semidefinite relaxations for sparse principal components , 2008, 2008 IEEE International Symposium on Information Theory.
[8] Jean-Christophe Mourrat,et al. Hamilton–Jacobi equations for finite-rank matrix inference , 2019, The Annals of Applied Probability.
[9] Michael I. Jordan,et al. Finite Size Corrections and Likelihood Ratio Fluctuations in the Spiked Wigner Model , 2017, ArXiv.
[10] S. Frick,et al. Compressed Sensing , 2014, Computer Vision, A Reference Guide.
[11] Florent Krzakala,et al. Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications , 2017, ArXiv.
[12] S. Péché,et al. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices , 2004, math/0403022.
[13] Marc Lelarge,et al. Fundamental limits of symmetric low-rank matrix estimation , 2016, Probability Theory and Related Fields.
[14] Dustin G. Mixon,et al. SUNLayer: Stable denoising with generative networks , 2018, ArXiv.
[15] G. Parisi,et al. Recipes for metastable states in spin glasses , 1995 .
[16] Vladislav Voroninski,et al. Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk , 2017, IEEE Transactions on Information Theory.
[17] J. Lee,et al. Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population , 2014, 1409.4979.
[18] Satish Babu Korada,et al. Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph , 2009 .
[19] Galen Reeves. Additivity of information in multilayer networks via additive Gaussian noise transforms , 2017, 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton).
[20] Florent Krzakala,et al. Estimation in the Spiked Wigner Model: A Short Proof of the Replica Formula , 2018, 2018 IEEE International Symposium on Information Theory (ISIT).
[21] Gábor Lugosi,et al. Concentration Inequalities - A Nonasymptotic Theory of Independence , 2013, Concentration Inequalities.
[22] Elchanan Mossel,et al. Spectral redemption in clustering sparse networks , 2013, Proceedings of the National Academy of Sciences.
[23] Sundeep Rangan,et al. Iterative estimation of constrained rank-one matrices in noise , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.
[24] Andrea Montanari,et al. Sparse PCA via Covariance Thresholding , 2013, J. Mach. Learn. Res..
[25] Nicolas Macris,et al. Optimal errors and phase transitions in high-dimensional generalized linear models , 2017, Proceedings of the National Academy of Sciences.
[26] Andrea Montanari,et al. Information-theoretically optimal sparse PCA , 2014, 2014 IEEE International Symposium on Information Theory.
[27] Adel Javanmard,et al. State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling , 2012, ArXiv.
[28] Léo Miolane. Fundamental limits of low-rank matrix estimation , 2017, 1702.00473.
[29] H. Nishimori. Statistical Physics of Spin Glasses and Information Processing , 2001 .
[30] Ankur Moitra,et al. Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models , 2018, The Annals of Statistics.
[31] Ankur Moitra,et al. Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization , 2016, ArXiv.
[32] Vladislav Voroninski,et al. Phase Retrieval Under a Generative Prior , 2018, NeurIPS.
[33] Florent Krzakala,et al. Phase transitions in sparse PCA , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).
[34] Nicolas Macris,et al. Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula , 2016, NIPS.
[35] Sundeep Rangan,et al. Inference in Deep Networks in High Dimensions , 2017, 2018 IEEE International Symposium on Information Theory (ISIT).
[36] Yoshua Bengio,et al. Generative Adversarial Nets , 2014, NIPS.
[37] Florent Krzakala,et al. Multi-layer generalized linear estimation , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).
[38] Florent Krzakala,et al. Mutual information in rank-one matrix estimation , 2016, 2016 IEEE Information Theory Workshop (ITW).
[39] H. Weyl. Inequalities between the Two Kinds of Eigenvalues of a Linear Transformation. , 1949, Proceedings of the National Academy of Sciences of the United States of America.
[40] Thomas M. Cover,et al. Elements of Information Theory , 2005 .
[41] Florent Krzakala,et al. Inferring sparsity: Compressed sensing using generalized restricted Boltzmann machines , 2016, 2016 IEEE Information Theory Workshop (ITW).
[42] Philippe Rigollet,et al. Computational Lower Bounds for Sparse PCA , 2013, ArXiv.
[43] Francis R. Bach,et al. Structured Sparse Principal Component Analysis , 2009, AISTATS.
[44] Andrea Montanari,et al. State Evolution for Approximate Message Passing with Non-Separable Functions , 2017, Information and Inference: A Journal of the IMA.
[45] Alexandros G. Dimakis,et al. Compressed Sensing using Generative Models , 2017, ICML.
[46] A. Montanari,et al. Asymptotic mutual information for the balanced binary stochastic block model , 2016 .
[47] Raj Rao Nadakuditi,et al. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices , 2009, 0910.2120.
[48] Richard G. Baraniuk,et al. From Denoising to Compressed Sensing , 2014, IEEE Transactions on Information Theory.
[49] David J. Field,et al. Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.
[50] O. Johnson. Free Random Variables , 2004 .
[51] N. Macris,et al. The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference , 2018, Probability Theory and Related Fields.
[52] E. Wigner. Characteristic Vectors of Bordered Matrices with Infinite Dimensions I , 1955 .
[53] Roland Vollgraf,et al. Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms , 2017, ArXiv.
[54] F. Guerra. Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model , 2002, cond-mat/0205123.
[55] J. W. Silverstein,et al. Analysis of the limiting spectral distribution of large dimensional random matrices , 1995 .
[56] Nicolas Macris,et al. Entropy and mutual information in models of deep neural networks , 2018, NeurIPS.