Volume ratio, sparsity, and minimaxity under unitarily invariant norms

Zongming Ma, Yihong Wu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents a non-asymptotic study of the minimax estimation of high-dimensional mean and covariance matrices. Based on the convex geometry of finite-dimensional Banach spaces, we develop a unified volume ratio approach for determining minimax estimation rates of unconstrained mean and covariance matrices under all unitarily invariant norms. We also establish the rate for estimating mean matrices with group sparsity, where the sparsity constraint introduces an additional term in the rate whose dependence on the norm differs completely from the rate of the unconstrained counterpart.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages1027-1031
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/TerritoryTurkey
CityIstanbul
Period7/7/137/12/13

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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