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We study the algorithmic thresholds for principal component analysis of Gaussian $k$-tensors with a planted rank-one spike, via Langevin dynamics and gradient descent.
Positive definite functions on spheres
Issac J. Schoenberg · 1942
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Markov processes
Stewart N. Ethier and Thomas G. Kurtz · 1986
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Multidimensional diffusion processes
Daniel W. Stroock and S. R. Srinivasa Varadhan · 1997
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p > 2 p>2 spin glasses with first-order ferromagnetic transitions
Peter Gillin and David Sherrington · 2000
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On the distribution of the largest principal component
Iain Johnstone · 2000
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Stochastic analysis on manifolds
Elton P. Hsu · 2002
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, Sandrine Péché, et al · 2005
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The largest eigenvalue of small rank perturbations of hermitian random matrices
S. Péché · 2006
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Large deviations for the largest eigenvalue of rank one deformations of gaussian ensembles
Mylène Maida · 2007
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The largest eigenvalues of finite rank deformation of large wigner matrices: convergence and nonuniversality of the fluctuations
Mireille Capitaine, Catherine Donati-Martin, Delphine Féral, et al · 2009
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Differential topology
Victor Guillemin and Alan Pollack · 2010
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Large deviations of the extreme eigenvalues of random deformations of matrices
F. Benaych-Georges, A. Guionnet, and M. Maida · 2012
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Complexity of random smooth functions on the high-dimensional sphere
Antonio Auffinger and Gérard Ben Arous · 2013
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Random matrices and complexity of spin glasses
Antonio Auffinger, Gérard Ben Arous, and Jiří Černý · 2013
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Optimal detection of sparse principal components in high dimension
Quentin Berthet and Philippe Rigollet · 2013
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Most tensor problems are np-hard
Christopher J. Hillar and Lek-Heng Lim · 2013
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A statistical model for tensor pca
Emile Richard and Andrea Montanari · 2014
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Tensor principal component analysis via sum-of-square proofs
Samuel B Hopkins, Jonathan Shi, and David Steurer · 2015
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Statistical physics of inference: Thresholds and algorithms
Lenka Zdeborová and Florent Krzakala · 2016
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The landscape of the spiked tensor model
Gerard Ben Arous, Song Mei, Andrea Montanari, and Mihai Nica · 2017
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Phase transition in the spiked random tensor with rademacher prior
Wei-Kuo Chen · 2017
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High dimensional regression with binary coefficients. estimating squared error and a phase transtition
David Gamarnik and Ilias Zadik · 2017
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On the optimization landscape of tensor decompositions
Rong Ge and Tengyu Ma · 2017
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Proof of the achievability conjectures for the general stochastic block model
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Bounding flows for spherical spin glass dynamics
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Spectral gap estimates in mean field spin glasses
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