Extremal bounds for Gaussian trace estimation Article Swipe
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Eric J. Hallman
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YOU?
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· 2024
· Open Access
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· DOI: https://doi.org/10.48550/arxiv.2411.15454
· OA: W4404986473
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.15454
· OA: W4404986473
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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