On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912081207361536 |
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| author | Horesh, Lior Kalantzis, Vasileios Lu, Yingdong Nowicki, Tomasz |
| author_facet | Horesh, Lior Kalantzis, Vasileios Lu, Yingdong Nowicki, Tomasz |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_16455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices Horesh, Lior Kalantzis, Vasileios Lu, Yingdong Nowicki, Tomasz Statistics Theory Numerical Analysis Probability 60-08, 65C05, 65F35 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. |
| title | On The Variance of Schatten $p$-Norm Estimation with Gaussian Sketching Matrices |
| topic | Statistics Theory Numerical Analysis Probability 60-08, 65C05, 65F35 |
| url | https://arxiv.org/abs/2410.16455 |