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We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data.
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A practical algorithm for the determination of phase from image and diffraction plane pictures
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Maximum likelihood from incomplete data via the EM algorithm
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Phase retrieval algorithms: A comparison
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On Milman’s inequality and random subspaces which escape through a mesh in
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On convergence properties of the EM algorithm for Gaussian mixtures
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A view of the EM algorithm that justifies incremental, sparse, and other variants
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Moment inequalities for functions of independent random variables
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Condition numbers of Gaussian random matrices
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Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2006
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The Lasso with general Gaussian designs with applications to hypothesis testing
M. Celentano, A. Montanari, and Y. Wei · 2007
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Message-passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
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M. Stojnic · 2009
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Asymptotic behavior of adversarial training in binary classification
H. Taheri, R. Pedarsani, and C. Thrampoulidis · 2010
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The Lasso risk for Gaussian matrices
M. Bayati and A. Montanari · 2011
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The noise-sensitivity phase transition in compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2011
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A generalized linear model with “Gaussian” regressor variables
D. R. Brillinger · 2012
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High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity
P.-L. Loh and M. J. Wainwright · 2012
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Noisy matrix completion using alternating minimization
S. Gunasekar, A. Acharya, N. Gaur, and J. Ghosh · 2013
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Probability in Banach Spaces: Isoperimetry and processes
M. Ledoux and M. Talagrand · 2013
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Statistical estimation: From denoising to sparse regression and hidden cliques
A. Montanari · 2013
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The squared-error of generalized Lasso: A precise analysis
S. Oymak, C. Thrampoulidis, and B. Hassibi · 2013
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Living on the edge: Phase transitions in convex programs with random data
D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp · 2014
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Fast matrix completion without the condition number
M. Hardt and M. Wootters · 2014
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Alternating minimization for mixed linear regression
X. Yi, C. Caramanis, and S. Sanghavi · 2014
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Universality in polytope phase transitions and message passing algorithms
M. Bayati, M. Lelarge, and A. Montanari · 2015
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Phase retrieval via Wirtinger flow: Theory and algorithms
E. J. Candes, X. Li, and M. Soltanolkotabi · 2015
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Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima
P.-L. Loh and M. J. Wainwright · 2015
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Phase retrieval using alternating minimization
P. Netrapalli, P. Jain, and S. Sanghavi · 2015
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Learning sparsely used overcomplete dictionaries via alternating minimization
A. Agarwal, A. Anandkumar, P. Jain, and P. Netrapalli · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
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Statistical and computational guarantees of Lloyd’s algorithm and its variants
Y. Lu and H. H. Zhou · 2016
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Fast and reliable parameter estimation from nonlinear observations
S. Oymak and M. Soltanolkotabi · 2016
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The generalized Lasso with non-linear observations
Y. Plan and R. Vershynin · 2016
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Guaranteed matrix completion via non-convex factorization
R. Sun and Z.-Q. Luo · 2016
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Recovering structured signals in high dimensions via non-smooth convex optimization: Precise performance analysis
C. Thrampoulidis · 2016
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Global convergence of the EM algorithm for mixtures of two component linear regression
J. Kwon, W. Qian, C. Caramanis, Y. Chen, and D. Davis · 2019
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Breaking the gridlock in mixture-of-experts: Consistent and efficient algorithms
A. Makkuva, P. Viswanath, S. Kannan, and S. Oh · 2019
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A. Montanari, F. Ruan, Y. Sohn, and J. Yan · 2019
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The impact of regularization on high-dimensional logistic regression
F. Salehi, E. Abbasi, and B. Hassibi · 2019
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A modern maximum-likelihood theory for high-dimensional logistic regression
P. Sur and E. J. Candès · 2019
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J. Xu, D. J. Hsu, and A. Maleki · 2016
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Statistical guarantees for the EM algorithm: From population to sample-based analysis
S. Balakrishnan, M. J. Wainwright, and B. Yu · 2017
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Ten steps of EM suffice for mixtures of two Gaussians
C. Daskalakis, C. Tzamos, and M. Zampetakis · 2017
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Phaseless recovery using the Gauss–Newton method
B. Gao and Z. Xu · 2017
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Fast, sample-efficient algorithms for structured phase retrieval
G. Jagatap and C. Hegde · 2017
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Non-convex optimization for machine learning
P. Jain and P. Kar · 2017
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Sharp time–data tradeoffs for linear inverse problems
S. Oymak, B. Recht, and M. Soltanolkotabi · 2017
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High-dimensional statistics: A non-asymptotic viewpoint , volume 48
M. J. Wainwright · 2019
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Does SLOPE outperform bridge regression?
S. Wang, H. Weng, and A. Maleki · 2019
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Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in
Y. Wu and H. H. Zhou · 2019
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Generalization error in high-dimensional perceptrons: Approaching bayes error with convex optimization
B. Aubin, Y. Lu, F. Krzakala, and L. Zdeborova · 2020
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The nonsmooth landscape of phase retrieval
D. Davis, D. Drusvyatskiy, and C. Paquette · 2020
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A precise performance analysis of learning with random features
O. Dhifallah and Y. M. Lu · 2020
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Singularity, misspecification and the convergence rate of EM
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Alternating minimization converges super-linearly for mixed linear regression
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Max-affine regression with universal parameter estimation for small-ball designs
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Instability, computational efficiency and statistical accuracy
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Precise statistical analysis of classification accuracies for adversarial training
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Precise tradeoffs in adversarial training for linear regression
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A precise high-dimensional asymptotic theory for boosting and minimum-
T. Liang and P. Sur · 2020
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Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution
C. Ma, K. Wang, Y. Chi, and Y. Chen · 2020
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Phase retrieval in high dimensions: Statistical and computational phase transitions
A. Maillard, B. Loureiro, F. Krzakala, and L. Zdeborová · 2020
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Halting time is predictable for large models: A universality property and average-case analysis
C. Paquette, B. van Merriënboer, E. Paquette, and F. Pedregosa · 2020
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Phase retrieval using alternating minimization in a batch setting
T. Zhang · 2020
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From symmetry to geometry: Tractable nonconvex problems
Y. Zhang, Q. Qu, and J. Wright · 2020
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Provable benefits of overparameterization in model compression: From double descent to pruning neural networks
X. Chang, Y. Li, S. Oymak, and C. Thrampoulidis · 2021
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Low-rank matrix recovery with composite optimization: Good conditioning and rapid convergence
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A model of double descent for high-dimensional binary linear classification
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A unifying tutorial on approximate message passing
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On the precise error analysis of support vector machines
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Homeomorphic-invariance of EM: Non-asymptotic convergence in KL divergence for exponential families via mirror descent
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The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning
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