# Compressed Covariance Estimation With Automated Dimension Learning

## TL;DR

This paper introduces a scalable method for covariance matrix estimation that combines low-rank and diagonal structures, utilizing data compression and an automated dimension learning framework based on Stein's Unbiased Risk Estimation.

## Contribution

It presents a novel covariance estimation technique that does not require the low-rank component to be sparse, with an automated dimension selection method.

## Key findings

- Effective in high-dimensional settings
- Scalable and computationally efficient
- Outperforms existing methods in simulations

## 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.