Compressed Covariance Estimation with Automated Dimension Learning

Gautam Sabnis (), Debdeep Pati and Anirban Bhattacharya
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Gautam Sabnis: University of Michigan
Debdeep Pati: Texas A&M University
Anirban Bhattacharya: Texas A&M University

Sankhya A: The Indian Journal of Statistics, 2019, vol. 81, issue 2, No 9, 466-481

Abstract: Abstract We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed space, and lifts it back to the ambient space via a decompression operation. A salient feature of our approach relative to existing literature on combining sparsity and low-rank structures in covariance matrix estimation is that we do not require the low-rank component to be sparse. A principled framework for estimating the compressed dimension using Stein’s Unbiased Risk Estimation theory is demonstrated. Experimental simulation results demonstrate the efficacy and scalability of our proposed approach.

Keywords: Compressed sensing; Dimension reduction; Low-rank; Factor model; Spiked covariance models; SURE; Primary 62J10; Secondary 62H12 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13171-018-0134-x

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