  Multivariate regression model is a natural generalization of the classical
univari- ate regression model for fitting multiple responses. In this paper, we
propose a high- dimensional multivariate conditional regression model for
constructing sparse estimates of the multivariate regression coefficient 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 coefficient 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
effectiveness 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.
