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arXiv · 2410.16455

On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices

Lior Horesh·Vasileios Kalantzis·Yingdong Lu·Tomasz Nowicki
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Abstract

Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the quality of such estimators is to consider the variance over the total number of observations. In this paper we present a procedure to compute the variance of the estimator proposed by Kong and Valiant [Ann. Statist. 45 (5), pp. 2218 - 2247] for the case of Gaussian random vectors and provide a sharper bound than previously available.

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BibTeXRIS

Lior Horesh, Vasileios Kalantzis, Yingdong Lu, Tomasz Nowicki. 2024-10-21. On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices. https://arxiv.org/abs/2410.16455

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