Compressed Covariance Estimation With Automated Dimension Learning
Methodology
2017-04-04 v1
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.
Cite
@article{arxiv.1704.00247,
title = {Compressed Covariance Estimation With Automated Dimension Learning},
author = {Gautam Sabnis and Debdeep Pati and Anirban Bhattacharya},
journal= {arXiv preprint arXiv:1704.00247},
year = {2017}
}