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- W4287637269 abstract "We study the problem of estimating the trace of a matrix $A$ that can only be accessed through matrix-vector multiplication. We introduce a new randomized algorithm, Hutch++, which computes a $(1 pm epsilon)$ approximation to $tr(A)$ for any positive semidefinite (PSD) $A$ using just $O(1/epsilon)$ matrix-vector products. This improves on the ubiquitous Hutchinson's estimator, which requires $O(1/epsilon^2)$ matrix-vector products. Our approach is based on a simple technique for reducing the variance of Hutchinson's estimator using a low-rank approximation step, and is easy to implement and analyze. Moreover, we prove that, up to a logarithmic factor, the complexity of Hutch++ is optimal amongst all matrix-vector query algorithms, even when queries can be chosen adaptively. We show that it significantly outperforms Hutchinson's method in experiments. While our theory mainly requires $A$ to be positive semidefinite, we provide generalized guarantees for general square matrices, and show empirical gains in such applications." @default.
- W4287637269 created "2022-07-25" @default.
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- W4287637269 date "2020-10-19" @default.
- W4287637269 modified "2023-09-27" @default.
- W4287637269 title "Hutch++: Optimal Stochastic Trace Estimation" @default.
- W4287637269 doi "https://doi.org/10.48550/arxiv.2010.09649" @default.
- W4287637269 hasPublicationYear "2020" @default.
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