Efron-Stein Inequalities for Random Matrices
Daniel Paulin, Lester Mackey, Joel A. Tropp
TL;DR
This paper develops new concentration inequalities for random matrices using the Efron-Stein framework and exchangeable pairs, extending previous inequalities to matrix-valued random variables.
Contribution
It introduces novel matrix concentration inequalities based on the Efron-Stein method and exchangeable pairs, advancing the theoretical understanding of random matrix behavior.
Findings
Derived new matrix concentration inequalities
Extended Efron-Stein inequalities to matrices
Provided proofs using exchangeable pairs method
Abstract
This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.
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Taxonomy
TopicsRandom Matrices and Applications · Point processes and geometric inequalities · Stochastic processes and statistical mechanics