Nonparametric estimation of low rank matrix valued function

DOI10.1214/19-EJS1582zbMath1429.62194arXiv1802.06292MaRDI QIDQ2326073

Yanyan Li

Publication date: 4 October 2019

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.06292

zbMATH Keywords

model selectionmatrix completionminimax lower boundnonparametric estimationlow ranklocal polynomial estimatornuclear norm penalization

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Estimation in multivariate analysis (62H12) Nonparametric estimation (62G05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Von Neumann entropy penalization and low-rank matrix estimation
• Estimation of high-dimensional low-rank matrices
• Oracle inequalities in empirical risk minimization and sparse recovery problems. École d'Été de Probabilités de Saint-Flour XXXVIII-2008.
• Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
• User-friendly tail bounds for sums of random matrices
• Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors
• Optimal pointwise adaptive methods in nonparametric estimation
• Model selection in nonparametric regression
• A Bennett concentration inequality and its application to suprema of empirical processes
• Matrix estimation by universal singular value thresholding
• Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Exact matrix completion via convex optimization
• Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
• A Singular Value Thresholding Algorithm for Matrix Completion
• Matrix completion via an alternating direction method
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Strong converse for identification via quantum channels
• On a Problem of Adaptive Estimation in Gaussian White Noise
• On the Tchebychef Inequality of Bernstein
• Sharp Oracle Inequalities in Low Rank Estimation
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation
• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• New concentration inequalities in product spaces