Dimension-free bounds for sums of independent matrices and simple tensors via the variational principle

DOI10.1214/23-ejp1021arXiv2108.08198OpenAlexW3196234164MaRDI QIDQ6186442

Nikita Zhivotovskiy

Publication date: 2 February 2024

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

Full work available at URL: https://arxiv.org/abs/2108.08198

zbMATH Keywords

random matricesconcentration inequalitieslog-concave measuressample covarianceeffective rank

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Inequalities involving eigenvalues and eigenvectors (15A42) Analysis of variance and covariance (ANOVA) (62J10)

Cites Work

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• Geometric median and robust estimation in Banach spaces
• The lower tail of random quadratic forms with applications to ordinary least squares
• Covariance estimation for distributions with \({2+\varepsilon}\) moments
• Estimating the covariance of random matrices
• Concentration inequalities and moment bounds for sample covariance operators
• Robust linear least squares regression
• User-friendly tail bounds for sums of random matrices
• Approximating the moments of marginals of high-dimensional distributions
• A tail inequality for quadratic forms of subgaussian random vectors
• \(L_{p}\)-moments of random vectors via majorizing measures
• Concentration of mass on convex bodies
• A note on the Hanson-Wright inequality for random vectors with dependencies
• Sub-Gaussian estimators of the mean of a random vector
• Robust dimension-free Gram operator estimates
• Challenging the empirical mean and empirical variance: a deviation study
• Approximating \(L_p\) unit balls via random sampling
• Concentration inequalities for polynomials in \(\alpha\)-sub-exponential random variables
• Uniform Hanson-Wright type concentration inequalities for unbounded entries via the entropy method
• Robust covariance estimation under \(L_4\)-\(L_2\) norm equivalence
• Concentration inequalities for random tensors
• Hadamard products and moments of random vectors
• Mean estimation and regression under heavy-tailed distributions: A survey
• On some problems concerning log-concave random vectors
• Structured random matrices
• On weakly bounded empirical processes
• Lower bounds on the smallest eigenvalue of a sample covariance matrix.
• The smallest singular value of random rectangular matrices with no moment assumptions on entries
• Asymptotically efficient estimation of smooth functionals of covariance operators
• Bounding the Smallest Singular Value of a Random Matrix Without Concentration
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• A Simple Tool for Bounding the Deviation of Random Matrices on Geometric Sets
• Upper and Lower Bounds for Stochastic Processes
• A Short Proof of Paouris' Inequality
• Concentration property on probability spaces.

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