Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression

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.