Extremal bounds for Gaussian trace estimation

Eric Hallman

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arXiv · 2411.15454

Extremal bounds for Gaussian trace estimation

Eric Hallman

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Abstract

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.

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BibTeX RIS

Eric Hallman. 2024-11-23. Extremal bounds for Gaussian trace estimation. https://arxiv.org/abs/2411.15454

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