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Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems.
Computational hardness of certifying bounds on constrained pca problems
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Subexponential-time algorithms for sparse PCA
Ding, Y., Kunisky, D., Wein, A. S., and Bandeira, A. S. (2019) · 1907
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Statistical and computational trade-offs in estimation of sparse principal components
Wang, T., Berthet, Q., and Samworth, R. J. (2016) · 1930
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On the distribution of the largest eigenvalue in principal components analysis
Johnstone, I. M. (2001) · 2001
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Concentration inequalities and model selection: Ecole d’Eté de Probabilités de Saint-Flour XXXIII-2003
Massart, P. (2007) · 2003
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A direct formulation for sparse PCA using semidefinite programming
d’Aspremont, A., Ghaoui, L., Jordan, M., and Lanckriet, G. (2004) · 2004
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
Baik, J., Arous, G. B., and Péché, S. (2005) · 2005
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The largest eigenvalue of small rank perturbations of hermitian random matrices
Péché, S. (2006) · 2006
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Sparse principal component analysis
Zou, H., Hastie, T., and Tibshirani, R. (2006) · 2006
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Phase retrieval via Wirtinger flow: Theory and algorithms
Candes, E. J., Li, X., and Soltanolkotabi, M. (2015) · 2007
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The Lasso with general Gaussian designs with applications to hypothesis testing
Celentano, M., Montanari, A., and Wei, Y. (2020) · 2007
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The largest eigenvalue of rank one deformation of large wigner matrices
Féral, D. and Péché, S. (2007) · 2007
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High-dimensional analysis of semidefinite relaxations for sparse principal components
Amini, A. A. and Wainwright, M. J. (2008) · 2008
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Central limit theorems for eigenvalues in a spiked population model
Bai, Z. and Yao, J.-f. (2008) · 2008
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On the high-temperature phase of the sherrington-kirkpatrick model
Bolthausen, E. (2009) · 2009
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The largest eigenvalues of finite rank deformation of large wigner matrices: convergence and nonuniversality of the fluctuations
Capitaine, M., Donati-Martin, C., and Féral, D. (2009) · 2009
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Message-passing algorithms for compressed sensing
Donoho, D. L., Maleki, A., and Montanari, A. (2009) · 2009
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Universality laws for high-dimensional learning with random features
Hu, H. and Lu, Y. M. (2020) · 2009
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On consistency and sparsity for principal components analysis in high dimensions
Johnstone, I. M. and Lu, A. Y. (2009) · 2009
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A message-passing receiver for bicm-ofdm over unknown clustered-sparse channels
Schniter, P. (2011) · 2011
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Angular synchronization by eigenvectors and semidefinite programming
Singer, A. (2011) · 2011
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A tail inequality for quadratic forms of subgaussian random vectors
Hsu, D., Kakade, S., and Zhang, T. (2012) · 2012
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Eigenvalues of deformed random matrices
Peng, M. (2012) · 2012
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Iterative estimation of constrained rank-one matrices in noise
Rangan, S. and Fletcher, A. K. (2012) · 2012
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Minimax rates of estimation for sparse PCA in high dimensions
Vu, V. and Lei, J. (2012) · 2012
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Information-theoretically optimal compressed sensing via spatial coupling and approximate message passing
Donoho, D. L., Javanmard, A., and Montanari, A. (2013) · 2013
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State evolution for general approximate message passing algorithms, with applications to spatial coupling
Javanmard, A. and Montanari, A. (2013) · 2013
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The isotropic semicircle law and deformation of Wigner matrices
Knowles, A. and Yin, J. (2013) · 2013
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Sparse principal component analysis and iterative thresholding
Ma, Z. (2013) · 2013
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Hanson-Wright inequality and sub-gaussian concentration
Rudelson, M. and Vershynin, R. (2013) · 2013
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Fantope projection and selection: A near-optimal convex relaxation of sparse PCA
Vu, V. Q., Cho, J., Lei, J., and Rohe, K. (2013) · 2013
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Information-theoretically optimal sparse PCA
Deshpande, Y. and Montanari, A. (2014a) · 2014
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Cone-constrained principal component analysis
Deshpande, Y., Montanari, A., and Richard, E. (2014) · 2014
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Scalable inference for neuronal connectivity from calcium imaging
Fletcher, A. K. and Rangan, S. (2014) · 2014
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Compressive phase retrieval via generalized approximate message passing
Schniter, P. and Rangan, S. (2014) · 2014
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Universality in polytope phase transitions and message passing algorithms
Bayati, M., Lelarge, M., and Montanari, A. (2015) · 2015
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Optimal estimation and rank detection for sparse spiked covariance matrices
Cai, T., Ma, Z., and Wu, Y. (2015) · 2015
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Variance breakdown of huber (m)-estimators: n / p → ( 1 , ∞ ) n/p\rightarrow(1,\infty)
Donoho, D. L. and Montanari, A. (2015) · 2015
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Do semidefinite relaxations solve sparse PCA up to the information limit?
Krauthgamer, R., Nadler, B., and Vilenchik, D. (2015) · 2015
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Phase transitions in sparse PCA
Fundamental limits of symmetric low-rank matrix estimation
Lelarge, M. and Miolane, L. (2019) · 2019
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The replica-symmetric prediction for random linear estimation with gaussian matrices is exact
Reeves, G. and Pfister, H. D. (2019) · 2019
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A modern maximum-likelihood theory for high-dimensional logistic regression
Sur, P. and Candès, E. J. (2019) · 2019
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The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled chi-square
Sur, P., Chen, Y., and Candès, E. J. (2019) · 2019
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High-dimensional statistics: A non-asymptotic viewpoint
Wainwright, M. J. (2019) · 2019
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The geometry of hypothesis testing over convex cones: Generalized likelihood ratio tests and minimax radii
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Lesieur, T., Krzakala, F., and Zdeborová, L. (2015) · 2015
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Non-negative principal component analysis: Message passing algorithms and sharp asymptotics
Montanari, A. and Richard, E. (2015) · 2015
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Sharp nonasymptotic bounds on the norm of random matrices with independent entries
Bandeira, A. S. and Van Handel, R. (2016) · 2016
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The mutual information in random linear estimation
Barbier, J., Dia, M., Macris, N., and Krzakala, F. (2016) · 2016
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Onsager-corrected deep learning for sparse linear inverse problems
Borgerding, M. and Schniter, P. (2016) · 2016
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High dimensional robust m-estimation: Asymptotic variance via approximate message passing
Donoho, D. and Montanari, A. (2016) · 2016
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Phase transitions in semidefinite relaxations
Javanmard, A., Montanari, A., and Ricci-Tersenghi, F. (2016) · 2016
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Wei, Y., Wainwright, M. J., and Guntuboyina, A. (2019) · 2019
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Exact asymptotics for phase retrieval and compressed sensing with random generative priors
Aubin, B., Loureiro, B., Baker, A., Krzakala, F., and Zdeborová, L. (2020) · 2020
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Algorithmic analysis and statistical estimation of SLOPE via approximate message passing
Bu, Z., Klusowski, J. M., Rush, C., and Su, W. J. (2020) · 2020
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Fundamental limits of detection in the spiked wigner model
El Alaoui, A., Krzakala, F., and Jordan, M. (2020) · 2020
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Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution
Ma, C., Wang, K., Chi, Y., and Chen, Y. (2020) · 2020
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All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation
Macris, N., Rush, C., et al. (2020) · 2020
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Singular vector and singular subspace distribution for the matrix denoising model
Bao, Z., Ding, X., and Wang, K. (2021) · 2021
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Local convexity of the TAP free energy and AMP convergence for z 2 z_{2} -synchronization
Celentano, M., Fan, Z., and Mei, S. (2021) · 2021
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Universality of approximate message passing algorithms
Chen, W.-K. and Lam, W.-K. (2021) · 2021
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Tackling small eigen-gaps: Fine-grained eigenvector estimation and inference under heteroscedastic noise
Cheng, C., Wei, Y., and Chen, Y. (2021) · 2021
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TAP free energy, spin glasses and variational inference
Fan, Z., Mei, S., and Montanari, A. (2021) · 2021
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The replica-symmetric free energy for Ising spin glasses with orthogonally invariant couplings
Fan, Z. and Wu, Y. (2021) · 2021
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Minimax estimation of linear functions of eigenvectors in the face of small eigen-gaps
Li, G., Cai, C., Poor, H. V., and Chen, Y. (2021) · 2021
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Minimum ℓ 1 \ell_{1} -norm interpolators: Precise asymptotics and multiple descent
Li, Y. and Wei, Y. (2021) · 2021
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Community detection with contextual multilayer networks
Ma, Z. and Nandy, S. (2021) · 2021
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PCA initialization for approximate message passing in rotationally invariant models
Mondelli, M. and Venkataramanan, R. (2021) · 2021
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Estimation of low-rank matrices via approximate message passing
Montanari, A. and Venkataramanan, R. (2021) · 2021
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Optimizing mean field spin glasses with external field
Sellke, M. (2021) · 2021
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Estimation in rotationally invariant generalized linear models via approximate message passing
Venkataramanan, R., Kögler, K., and Mondelli, M. (2021) · 2021
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Inference for heteroskedastic PCA with missing data
Yan, Y., Chen, Y., and Fan, J. (2021) · 2021
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Fundamental barriers to high-dimensional regression with convex penalties
Celentano, M. and Montanari, A. (2022) · 2022
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Universality of approximate message passing with semi-random matrices
Dudeja, R., Lu, Y. M., and Sen, S. (2022) · 2022
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Approximate message passing algorithms for rotationally invariant matrices
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A unifying tutorial on approximate message passing
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SDP achieves exact minimax optimality in phase synchronization
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Universality of approximate message passing algorithms and tensor networks
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Li, G., Fan, W., and Wei, Y. (2023) · 2023
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Deflated heteropca: Overcoming the curse of ill-conditioning in heteroskedastic PCA
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Matrix completion from noisy entries
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