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When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise.
A generalization of the method of maximum likelihood: Estimating a mixing distribution (abstract)
Herbert Robbins · 1950
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Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters
Jack Kiefer and Jacob Wolfowitz · 1956
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An empirical Bayes approach to statistics
Herbert Robbins · 1956
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Maximum likelihood estimation of a compound Poisson process
Leopold Simar · 1976
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Nonparametric maximum likelihood estimation of a mixing distribution
Nan Laird · 1978
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Mixtures of exponential distributions
Nicholas P Jewell · 1982
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The geometry of mixture likelihoods: a general theory
Bruce G Lindsay · 1983
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The geometry of mixture likelihoods, part II: the exponential family
Bruce G Lindsay · 1983
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Computer-assisted analysis of mixtures (CA MAN): statistical algorithms
Dankmar Bohning, Peter Schlattmann, and Bruce Lindsay · 1992
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Uniqueness of estimation and identifiability in mixture models
Bruce G Lindsay and Kathryn Roeder · 1993
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Loading and correlations in the interpretation of principal compenents
Jorge Cadima and Ian T Jolliffe · 1995
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Mixture models: theory, geometry and applications
Bruce G Lindsay · 1995
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Computer-assisted analysis of mixtures and applications: meta-analysis, disease mapping and others
Dankmar Böhning · 1999
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Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities
Subhashis Ghosal and Aad W van der Vaart · 2001
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On the distribution of the largest eigenvalue in principal components analysis
Iain M Johnstone · 2001
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Sparse principal component analysis for functional data
Arthur Yu Lu · 2002
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A modified principal component technique based on the LASSO
Ian T Jolliffe, Nickolay T Trendafilov, and Mudassir Uddin · 2003
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A CDMA multiuser detection algorithm on the basis of belief propagation
Yoshiyuki Kabashima · 2003
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Jinho Baik, Gérard Ben Arous, and Sandrine Péché · 2005
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A direct formulation for sparse PCA using semidefinite programming
Alexandre d’Aspremont, Laurent E Ghaoui, Michael I Jordan, and Gert R Lanckriet · 2005
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Eigenvalues of large sample covariance matrices of spiked population models
Jinho Baik and Jack W Silverstein · 2006
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Sparse principal component analysis
Hui Zou, Trevor Hastie, and Robert Tibshirani · 2006
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Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
Debashis Paul · 2007
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High-dimensional analysis of semidefinite relaxations for sparse principal components
Arash A Amini and Martin J Wainwright · 2008
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Central limit theorems for eigenvalues in a spiked population model
Zhidong Bai and Jianfeng Yao · 2008
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Convex clustering with exemplar-based models
Danial Lashkari and Polina Golland · 2008
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On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices
Xavier Mestre · 2008
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Finite sample approximation results for principal component analysis: A matrix perturbation approach
Boaz Nadler · 2008
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Message-passing algorithms for compressed sensing
David L Donoho, Arian Maleki, and Andrea Montanari · 2009
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On consistency and sparsity for principal components analysis in high dimensions
Iain M Johnstone and Arthur Yu Lu · 2009
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PCA consistency in high dimension, low sample size context
Sungkyu Jung and J Stephen Marron · 2009
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General maximum likelihood empirical Bayes estimation of normal means
Wenhua Jiang and Cun-Hui Zhang · 2009
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Generalized maximum likelihood estimation of normal mixture densities
Cun-Hui Zhang · 2009
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A singular value thresholding algorithm for matrix completion
Jian-Feng Cai, Emmanuel J Candès, and Zuowei Shen · 2010
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Integrating common and rare genetic variation in diverse human populations
International HapMap 3 Consortium · 2010
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2011
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Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices
Mireille Capitaine, Catherine Donati-Martin, Delphine Féral, and Maxime Février · 2011
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Generalized approximate message passing for estimation with random linear mixing
Sundeep Rangan · 2011
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Expectation-maximization Bernoulli-Gaussian approximate message passing
Non-negative principal component analysis: Message passing algorithms and sharp asymptotics
Andrea Montanari and Emile Richard · 2015
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A global reference for human genetic variation
The 1000 Genomes Project Consortium · 2015
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Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula
Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur, and Lenka Zdeborová · 2016
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On the principal components of sample covariance matrices
Alex Bloemendal, Antti Knowles, Horng-Tzer Yau, and Jun Yin · 2016
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Approximate nonparametric maximum likelihood inference for mixture models via convex optimization
Long Feng and Lee H Dicker · 2016
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Jeremy Vila and Philip Schniter · 2011
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The singular values and vectors of low rank perturbations of large rectangular random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2012
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On sample eigenvalues in a generalized spiked population model
Zhidong Bai and Jianfeng Yao · 2012
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Large-scale inference: Empirical Bayes methods for estimation, testing, and prediction
Bradley Efron · 2012
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Statistical-physics-based reconstruction in compressed sensing
Florent Krzakala, Marc Mézard, François Sausset, YF Sun, and Lenka Zdeborová · 2012
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Nonlinear shrinkage estimation of large-dimensional covariance matrices
Olivier Ledoit and Michael Wolf · 2012
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Iterative estimation of constrained rank-one matrices in noise
Sundeep Rangan and Alyson K Fletcher · 2012
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Phase transitions and sample complexity in Bayes-optimal matrix factorization
Yoshiyuki Kabashima, Florent Krzakala, Marc Mézard, Ayaka Sakata, and Lenka Zdeborová · 2016
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Asymptotic mutual information for the balanced binary stochastic block model
Yash Deshpande, Emmanuel Abbe, and Andrea Montanari · 2017
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Optimal shrinkage of singular values
Matan Gavish and David L Donoho · 2017
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Fundamental limits of low-rank matrix estimation: the non-symmetric case
Léo Miolane · 2017
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Asymptotics of empirical eigenstructure for high dimensional spiked covariance
Weichen Wang and Jianqing Fan · 2017
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Estimation in the spiked Wigner model: A short proof of the replica formula
Ahmed El Alaoui and Florent Krzakala · 2018
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Limiting eigenvectors of outliers for spiked information-plus-noise type matrices
Mireille Capitaine · 2018
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Mireille Capitaine and Catherine Donati-Martin · 2018
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PCA in high dimensions: An orientation
Iain M Johnstone and Debashis Paul · 2018
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Mutual information as a function of matrix snr for linear gaussian channels
Galen Reeves, Henry D Pfister, and Alex Dytso · 2018
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High-dimensional probability: An introduction with applications in data science
Roman Vershynin · 2018
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Glassy nature of the hard phase in inference problems
Fabrizio Antenucci, Silvio Franz, Pierfrancesco Urbani, and Lenka Zdeborová · 2019
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The adaptive interpolation method: A simple scheme to prove replica formulas in Bayesian inference
Jean Barbier and Nicolas Macris · 2019
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An instability in variational inference for topic models
Behrooz Ghorbani, Hamid Javadi, and Andrea Montanari · 2019
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Fundamental limits of symmetric low-rank matrix estimation
Marc Lelarge and Léo Miolane · 2019
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Edge universality of separable covariance matrices
Fan Yang · 2019
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Statistical inference for principal components of spiked covariance matrix
Zhigang Bao, Xiucai Ding, Jingming Wang, and Ke Wang · 2020
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Singular vector and singular subspace distribution for the matrix denoising model
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