Inference for low-rank tensors -- no need to debias

DOI10.1214/21-AOS2146zbMath1486.62165arXiv2012.14844OpenAlexW3116363844WikidataQ114060479 ScholiaQ114060479MaRDI QIDQ2131273

Dong Xia, Yuchen Zhou, Anru R. Zhang

Publication date: 25 April 2022

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

Full work available at URL: https://arxiv.org/abs/2012.14844

zbMATH Keywords

asymptotic distributionconfidence regionstatistical inferencetensor regressiontensor principal component analysis

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Asymptotic distribution theory in statistics (62E20) Multilinear algebra, tensor calculus (15A69)

Related Items (1)

Generalized Low-Rank Plus Sparse Tensor Estimation by Fast Riemannian Optimization

Uses Software

• Cross
• PhaseLift

Cites Work

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• Tensor Decompositions and Applications
• On asymptotically optimal confidence regions and tests for high-dimensional models
• Geometric inference for general high-dimensional linear inverse problems
• On tensor completion via nuclear norm minimization
• Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
• The sparsity and bias of the LASSO selection in high-dimensional linear regression
• Cross: efficient low-rank tensor completion
• Multilayer tensor factorization with applications to recommender systems
• On polynomial time methods for exact low-rank tensor completion
• Community detection on mixture multilayer networks via regularized tensor decomposition
• An optimal statistical and computational framework for generalized tensor estimation
• Tensor clustering with planted structures: statistical optimality and computational limits
• Statistical limits of spiked tensor models
• Uncertainty quantification for matrix compressed sensing and quantum tomography problems
• Normal approximation and confidence region of singular subspaces
• Generalized high-dimensional trace regression via nuclear norm regularization
• Phase transition in the spiked random tensor with Rademacher prior
• Rapid, robust, and reliable blind deconvolution via nonconvex optimization
• Low rank tensor recovery via iterative hard thresholding
• Convex regularization for high-dimensional multiresponse tensor regression
• Singular vector and singular subspace distribution for the matrix denoising model
• Orthogonal Tensor Decompositions
• Rank-One Approximation to High Order Tensors
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• A New Truncation Strategy for the Higher-Order Singular Value Decomposition
• High-Dimensional Covariance Decomposition into Sparse Markov and Independence Models
• Tensor decompositions for learning latent variable models
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Tensor SVD: Statistical and Computational Limits
• Eigenvectors of Orthogonally Decomposable Functions
• Spectral Algorithms for Tensor Completion
• Weighted Matrix Completion From Non-Random, Non-Uniform Sampling Patterns
• ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching
• Statistical Inferences of Linear Forms for Noisy Matrix Completion
• Sparse and Low-Rank Tensor Estimation via Cubic Sketchings
• The Landscape of the Spiked Tensor Model
• Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data
• Dynamic Tensor Clustering
• Confidence Region of Singular Subspaces for Low-Rank Matrix Regression
• Inference and uncertainty quantification for noisy matrix completion
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Tensor Regression with Applications in Neuroimaging Data Analysis
• Tensor product analysis of partial difference equations
• Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices
• Most Tensor Problems Are NP-Hard
• Provable Sparse Tensor Decomposition
• Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models

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