Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression

TL;DR

This paper introduces a joint regression-based approach for estimating sparse inverse covariance and partial correlation matrices in high-dimensional settings, ensuring positive semi-definiteness and providing theoretical guarantees.

Contribution

It proposes a novel two-stage estimation method that exploits linear regression connections, along with an efficient algorithm and non-asymptotic error bounds.

Findings

Effective on synthetic data

Demonstrates real-world applicability

Provides non-asymptotic estimation rates

Abstract

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation method wherein each individual feature is regressed on all other features while positive semi-definiteness is enforced simultaneously. We derive non-asymptotic estimation rates for both inverse covariance and partial correlation matrix estimation. An efficient proximal splitting algorithm for numerically computing the estimate is also dervied. The effectiveness of the proposed method is demonstrated on both synthetic and real-world data.