On the variance of Schatten p-norm estimation with Gaussian sketching matrices

Horesh Lior (), Kalantzis Vasileios (), Lu Yingdong () and Nowicki Tomasz ()
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Horesh Lior: IBM Research, 1101 Kitchawan Rd, Yorktown Heights, NY 10598, USA
Kalantzis Vasileios: IBM Research, 1101 Kitchawan Rd, Yorktown Heights, NY 10598, USA
Lu Yingdong: IBM Research, 1101 Kitchawan Rd, Yorktown Heights, NY 10598, USA
Nowicki Tomasz: IBM Research, 1101 Kitchawan Rd, Yorktown Heights, NY 10598, USA

Monte Carlo Methods and Applications, 2025, vol. 31, issue 2, 119-130

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 in [W. Kong and G. Valiant, Spectrum estimation from samples, Ann. Statist. 45 2017, 5, 2218–2247] for the case of Gaussian random vectors and provide a sharper bound than previously available.

Keywords: variance; Gaussian random vector (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2025-2006

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