Joint estimation of sparse multivariate regression and conditional graphical models
Multivariate regression model is a natural generalization of the classical univari- ate regression model for ?tting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coe?cient matrix that accounts for the dependency struc- ture among the multiple responses. The proposed method decomposes the multivariate regression problem into a series of penalized conditional log-likelihood of each response conditioned on the covariates and other responses. It allows simultaneous estimation of the sparse regression coe?cient matrix and the sparse inverse covariance matrix. The asymptotic selection consistency and normality are established for the diverging dimension of the covariates and number of responses. The e?ectiveness of the pro- posed method is also demonstrated in a variety of simulated examples as well as an application to the Glioblastoma multiforme cancer data.