Compressed Covariance Estimation With Automated Dimension Learning

2017/04/02 by Sabnis, Gautam, Pati, Debdeep, Bhattacharya, Anirban
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.1704.00247

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.

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