Subspace estimation from unbalanced and incomplete data matrices: \({\ell_{2,\infty}}\) statistical guarantees

DOI10.1214/20-AOS1986zbMath1471.62371arXiv1910.04267MaRDI QIDQ2039795

H. Vincent Poor, Yuxin Chen, Gen Li, Changxiao Cai, Yuejie Chi

Publication date: 5 July 2021

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.04267

zbMATH Keywords

principal component analysisspectral methodmissing dataspectral clusteringcovariance estimationtensor completionleave-one-out analysis

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Missing data (62D10)

Related Items

Biwhitening Reveals the Rank of a Count Matrix, Iterative Collaborative Filtering for Sparse Matrix Estimation, Nonconvex Low-Rank Tensor Completion from Noisy Data, Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution Under Random Designs, Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems, Community detection on mixture multilayer networks via regularized tensor decomposition, An \({\ell_p}\) theory of PCA and spectral clustering

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Consistency thresholds for the planted bisection model
• On tensor completion via nuclear norm minimization
• Sparse principal component analysis and iterative thresholding
• High-dimensional covariance matrix estimation with missing observations
• Reconstruction and estimation in the planted partition model
• Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance
• Angular synchronization by eigenvectors and semidefinite programming
• Spectral clustering and the high-dimensional stochastic blockmodel
• High-dimensional regression with noisy and missing data: provable guarantees with nonconvexity
• Community detection in sparse networks via Grothendieck's inequality
• Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data
• On sample eigenvalues in a generalized spiked population model
• Delocalization of eigenvectors of random matrices with independent entries
• Covariance regularization by thresholding
• Finite sample approximation results for principal component analysis: A matrix perturbation approach
• Weighted least squares fitting using ordinary least squares algorithms
• Random perturbation of low rank matrices: improving classical bounds
• On semidefinite relaxations for the block model
• Random Laplacian matrices and convex relaxations
• On the distribution of the largest eigenvalue in principal components analysis
• Adaptive covariance matrix estimation through block thresholding
• On polynomial time methods for exact low-rank tensor completion
• Implicit regularization in nonconvex statistical estimation: gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution
• Entrywise eigenvector analysis of random matrices with low expected rank
• Spectral method and regularized MLE are both optimal for top-\(K\) ranking
• The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics
• Matrix estimation by universal singular value thresholding
• Consistency of spectral clustering in stochastic block models
• Optimal estimation and rank detection for sparse spiked covariance matrices
• Robust and computationally feasible community detection in the presence of arbitrary outlier nodes
• Convexified modularity maximization for degree-corrected stochastic block models
• Sparse PCA: optimal rates and adaptive estimation
• Exact matrix completion via convex optimization
• Statistically optimal and computationally efficient low rank tensor completion from noisy entries
• Asymmetry helps: eigenvalue and eigenvector analyses of asymmetrically perturbed low-rank matrices
• Optimal Estimation and Completion of Matrices with Biclustering Structures
• Sparse Principal Component Analysis with Missing Observations
• Perturbation of Linear Forms of Singular Vectors Under Gaussian Noise
• Phase transitions in semidefinite relaxations
• Guaranteed Matrix Completion via Non-Convex Factorization
• Information Recovery From Pairwise Measurements
• Achieving Exact Cluster Recovery Threshold via Semidefinite Programming: Extensions
• Exact Recovery in the Stochastic Block Model
• Tensor completion and low-n-rank tensor recovery via convex optimization
• Oracle Inequalities for Local and Global Empirical Risk Minimizers
• A spectral heuristic for bisecting random graphs
• Graph Partitioning via Adaptive Spectral Techniques
• Community Detection and Stochastic Block Models
• An $\ell_{\infty}$ Eigenvector Perturbation Bound and Its Application to Robust Covariance Estimation
• Tensor SVD: Statistical and Computational Limits
• Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion
• Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing
• The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences
• Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography
• A Simple SVD Algorithm for Finding Hidden Partitions
• Asymptotic theory for estimating the singular vectors and values of a partially-observed low rank matrix with noise
• Near-Optimal Bounds for Phase Synchronization
• A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs
• Spectral Algorithms for Tensor Completion
• Covariance Matrix Estimation With Non Uniform and Data Dependent Missing Observations
• Optimal Bipartite Network Clustering
• Sparse and Low-Rank Tensor Estimation via Cubic Sketchings
• Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization
• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• Community detection thresholds and the weak Ramanujan property
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• Matrix Completion From a Few Entries
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Achieving Optimal Misclassification Proportion in Stochastic Block Model
• Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
• The Sup-norm Perturbation of HOSVD and Low Rank Tensor Denoising
• Low-rank matrix completion using alternating minimization
• Perturbation theory for pseudo-inverses
• Signal-plus-noise matrix models: eigenvector deviations and fluctuations