Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression
This work addresses a statistical estimation problem for high-dimensional data analysis, but it appears incremental as it builds on existing regression-based approaches.
The authors tackled the problem of estimating sparse high-dimensional inverse covariance and partial correlation matrices by developing a two-stage method that enforces positive semi-definiteness, achieving non-asymptotic estimation rates and demonstrating effectiveness on synthetic and real-world data.
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.