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For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime.
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Jonathan S Yedidia, William T Freeman, and Yair Weiss · 2003
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Amin Coja-Oghlan, Andreas Goerdt, and André Lanka · 2004
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Iain M Johnstone and Arthur Yu Lu · 2004
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Linear level Lasserre lower bounds for certain k-CSPs
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Graphical models, exponential families, and variational inference
Martin J Wainwright and Michael I Jordan · 2008
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David L Donoho, Arian Maleki, and Andrea Montanari · 2009
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Chris Godsil and Sung Y Song · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
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Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
Aurelien Decelle, Florent Krzakala, Cristopher Moore, and Lenka Zdeborová · 2011
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Aurelien Decelle, Florent Krzakala, Cristopher Moore, and Lenka Zdeborová · 2011
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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Antonio Auffinger, Gérard Ben Arous, and Jiří Černỳ · 2013
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Florent Krzakala, Cristopher Moore, Elchanan Mossel, Joe Neeman, Allan Sly, Lenka Zdeborová, and Pan Zhang · 2013
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, and Lenka Zdeborová · 2016
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An orthogonal basis for functions over a slice of the Boolean hypercube
Yuval Filmus · 2016
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Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
Samuel B Hopkins, Tselil Schramm, Jonathan Shi, and David Steurer · 2016
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Statistical limits of spiked tensor models
Amelia Perry, Alexander S Wein, and Afonso S Bandeira · 2016
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Spectral inference methods on sparse graphs: theory and applications
Alaa Saade · 2016
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Tensor decompositions for learning latent variable models
Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M Kakade, and Matus Telgarsky · 2014
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Belief propagation, robust reconstruction and optimal recovery of block models
Elchanan Mossel, Joe Neeman, and Allan Sly · 2014
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A statistical model for tensor PCA
Emile Richard and Andrea Montanari · 2014
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Spectral clustering of graphs with the Bethe Hessian
Alaa Saade, Florent Krzakala, and Lenka Zdeborová · 2014
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How to refute a random CSP
Sarah R Allen, Ryan O’Donnell, and David Witmer · 2015
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Non-backtracking spectrum of random graphs: community detection and non-regular ramanujan graphs
Charles Bordenave, Marc Lelarge, and Laurent Massoulié · 2015
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Analyzing tensor power method dynamics in overcomplete regime
Animashree Anandkumar, Rong Ge, and Majid Janzamin · 2017
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Johnson schemes and certain matrices with integral eigenvalues
Amanda Burcroff · 2017
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Phase transition in the spiked random tensor with rademacher prior
Wei-Kuo Chen · 2017
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The power of sum-of-squares for detecting hidden structures
Samuel B Hopkins, Pravesh K Kothari, Aaron Potechin, Prasad Raghavendra, Tselil Schramm, and David Steurer · 2017
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Statistical and computational phase transitions in spiked tensor estimation
Thibault Lesieur, Léo Miolane, Marc Lelarge, Florent Krzakala, and Lenka Zdeborová · 2017
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Strongly refuting random CSPs below the spectral threshold
Prasad Raghavendra, Satish Rao, and Tselil Schramm · 2017
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Algorithmic thresholds for tensor PCA
Gerard Ben Arous, Reza Gheissari, and Aukosh Jagannath · 2018
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Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
Jess Banks, Cristopher Moore, Roman Vershynin, Nicolas Verzelen, and Jiaming Xu · 2018
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Phase transition in random tensors with multiple spikes
Wei-Kuo Chen, Madeline Handschy, and Gilad Lerman · 2018
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Fundamental limits of detection in the spiked wigner model
Ahmed El Alaoui, Florent Krzakala, and Michael I Jordan · 2018
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Iterative reconstruction of rank-one matrices in noise
Alyson K Fletcher and Sundeep Rangan · 2018
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Statistical thresholds for tensor PCA
Aukosh Jagannath, Patrick Lopatto, and Leo Miolane · 2018
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Optimality and sub-optimality of PCA I: Spiked random matrix models
Amelia Perry, Alexander S Wein, Afonso S Bandeira, and Ankur Moitra · 2018
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Giulio Biroli, Chiara Cammarota, and Federico Ricci-Tersenghi · 2019
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Classical and quantum algorithms for tensor principal component analysis
Matthew B Hastings · 2019
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Dmitriy Kunisky, Alexander S Wein, and Afonso S Bandeira · 2019
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