An integrated precision matrix estimation for multivariate regression problems

Multi-response linear models and dependent features arise in many modern scientific problems. In this paper, we aim to learn the regression coefficients while simultaneously estimating the conditional independence relationships among the set of response vectors and predictors. The proposed method, named Integrated Precision Matrix Estimation (IPME), is formulated as a biconvex optimization problem. We solve this method via an efficient two-step minimization. The conditional independence structure of responses and predictors are estimated in an undirected graph in which the set of edges corresponds to the set of effective predictors. Numerical comparisons of the proposed method with several existing methods show that the method works effectively. We apply this method to financial data. Results show that IPME is successful in asset allocation selection. (C) 2022 Elsevier B.V. All rights reserved.