Sparse Estimation of Inverse Covariance and Partial Correlation Matrices via Joint Partial Regression

Samuel Erickson, Tobias Rydén

Abstract: We present a new method for estimating high-dimensional sparse partial correlation and inverse covariance 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 provide statistical rates of convergence for the proposed method which match, and improve upon, the state-of-the-art for inverse covariance and partial correlation matrix estimation, respectively. We also propose an efficient proximal splitting algorithm for numerically computing the estimate. The effectiveness of the proposed method is demonstrated on both synthetic and real-world data.