From Poincaré inequalities to nonlinear matrix concentration

Autor:	De Huang, Joel A. Tropp
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Statistics and Probability Matrix (mathematics) Pure mathematics symbols.namesake Trace (linear algebra) Dirichlet form Multivariate random variable Subadditivity symbols Poincaré inequality Matrix exponential Concentration inequality Mathematics
Popis:	This paper deduces exponential matrix concentration from a Poincare inequality via a short, conceptual argument. Among other examples, this theory applies to matrix-valued functions of a uniformly log-concave random vector. The proof relies on the subadditivity of Poincare inequalities and a chain rule inequality for the trace of the matrix Dirichlet form. It also uses a symmetrization technique to avoid difficulties associated with a direct extension of the classic scalar argument.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ac4ce4f6b93c06fe026a56eff248b9b6 https://resolver.caltech.edu/CaltechAUTHORS:20201218-154430753 Zobrazit plný text záznamu