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• W2144164089 abstract "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 analyse this approach, Levina & Vershynin (2011, Probab. Theory Related Fields) 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 log2p) 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 log5p) obtained by Levina and Vershynin." @default.
• W2144164089 created "2016-06-24" @default.
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• W2144164089 date "2012-05-15" @default.
• W2144164089 modified "2023-10-10" @default.
• W2144164089 title "The masked sample covariance estimator: an analysis using matrix concentration inequalities" @default.
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• W2144164089 doi "https://doi.org/10.1093/imaiai/ias001" @default.
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