Matrix Concentration Inequalities via the Method of Exchangeable Pairs

Abstract

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoe ding, Bernstein, Khintchine, and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.

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Document Details

Document Type
Technical Report
Publication Date
Jan 27, 2012
Accession Number
ADA563088

Entities

People

  • Brendan Farrell
  • Joel A. Tropp
  • Lester Mackey
  • Michael I. Jordan
  • Richard Y. Chen

Organizations

  • California Institute of Technology

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Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Compressed Sensing
  • Computations
  • Eigenvalues
  • Electrical Engineering
  • Equations
  • Functional Analysis
  • Identities
  • Inequalities
  • Information Processing
  • Mathematics
  • Polynomials
  • Probability
  • Quadratic Equations
  • Random Variables
  • Standards
  • Statistics

Fields of Study

  • Mathematics

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  • Linear Algebra