Extremal bounds for Gaussian trace estimation

Fuente: arXiv
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Autore principale: Hallman, Eric
Natura: Preprint
Pubblicazione: 2024
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author Hallman, Eric
author_facet Hallman, Eric
contents This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will have worse tail bounds. This is done for two families of matrices: positive semidefinite matrices with bounded effective rank, and indefinite matrices with bounded 2-norm and fixed Frobenius norm. In each case, the tail region is defined rigorously and is constant for a given family.
format Preprint
id arxiv_https___arxiv_org_abs_2411_15454
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Extremal bounds for Gaussian trace estimation
Hallman, Eric
Statistics Theory
Numerical Analysis
Probability
60E15, 60E07, 65C05
This work derives extremal tail bounds for the Gaussian trace estimator applied to a real symmetric matrix. We define a partial ordering on the eigenvalues, so that when a matrix has greater spectrum under this ordering, its estimator will have worse tail bounds. This is done for two families of matrices: positive semidefinite matrices with bounded effective rank, and indefinite matrices with bounded 2-norm and fixed Frobenius norm. In each case, the tail region is defined rigorously and is constant for a given family.
title Extremal bounds for Gaussian trace estimation
topic Statistics Theory
Numerical Analysis
Probability
60E15, 60E07, 65C05
url https://arxiv.org/abs/2411.15454