Improved bounds for randomized Schatten norm estimation of numerically low-rank matrices
In this work, we analyze the variance of a stochastic estimator for computing Schatten norms of matrices. The estimator extracts information from a single sketch of the matrix, that is, the product of the matrix with a few standard Gaussian random vectors. While this estimator has been proposed and...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
30.08.2024
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Subjects | |
Online Access | Get full text |
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Summary: | In this work, we analyze the variance of a stochastic estimator for computing
Schatten norms of matrices. The estimator extracts information from a single
sketch of the matrix, that is, the product of the matrix with a few standard
Gaussian random vectors. While this estimator has been proposed and used in the
literature before, the existing variance bounds are often pessimistic. Our work
provides a sharper upper bound on the variance and we also give estimates of
the variance that work well for numerically low-rank matrices. Our theoretical
findings are supported by numerical experiments, demonstrating that the new
bounds are significantly tighter than the existing ones. |
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DOI: | 10.48550/arxiv.2408.17414 |