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.

本文提出了一种高维多元回归模型，通过惩罚条件对每个响应变量对其他变量的依赖结构进行建模，以构造稀疏的多元回归系数矩阵估计，同时估计稀疏的逆协方差矩阵。该方法能够同时进行多元回归和协方差矩阵的估计，并在一个假设条件下得到渐近选择一致性与正态性，其有效性在多个模拟实验和对 Glioblastoma multiforme 的应用中得到验证。