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The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities

Chen, Richard Y. and Gittens, Alex and Tropp, Joel A. (2011) The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities. . (Submitted)

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Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is nearly sparse and to focus on estimating only the significant entries. To analyze this approach, Levina and Vershynin (2011) introduce a formalism called masked covariance estimation, where each entry of the sample covariance estimator is reweighted to reflect an a priori assessment of its importance. This paper provides a short analysis of the masked sample covariance estimator by means of a matrix concentration inequality. The main result applies to general distributions with at least four moments. Specialized to the case of a Gaussian distribution, the theory offers qualitative improvements over earlier work. For example, the new results show that n = O(B log^2 p) samples suffice to estimate a banded covariance matrix with bandwidth B up to a relative spectral-norm error, in contrast to the sample complexity n = O(B log^5 p) obtained by Levina and Vershynin.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Tropp, Joel A.0000-0003-1024-1791
Subject Keywords:Covariance estimation, matrix concentration inequality, matrix Khintchine inequality, matrix Rosenthal inequality, random matrix, Schur product
Classification Code:2010 Math Subject Classification. Primary: 60B20; Secondary: 62H12, 60F10, 60G50
Record Number:CaltechAUTHORS:20180831-112123699
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89334
Deposited By: George Porter
Deposited On:04 Sep 2018 14:32
Last Modified:03 Oct 2019 20:15

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