On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices
Statistics Theory
2024-10-23 v1 Numerical Analysis
Numerical Analysis
Probability
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2410.16455,
title = {On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices},
author = {Lior Horesh and Vasileios Kalantzis and Yingdong Lu and Tomasz Nowicki},
journal= {arXiv preprint arXiv:2410.16455},
year = {2024}
}