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Title: A convex optimization formulation for multivariate regression Authors:  Yunzhang Zhu - Ohio State University (United States) [presenting]
Abstract: Multivariate regression (or multi-task learning) concerns the task of predicting the value of multiple responses from a set of covariates. We will present a convex optimization formulation for high-dimensional multivariate linear regression under general error covariance structure. The main difficulty for simultaneous estimation of the regression coefficients and the error covariance lies in the fact that the negative log-likelihood function is not jointly convex. To overcome this difficulty, a new parameterization is proposed, under which the negative log-likelihood function is convex. It will be demonstrated that the new parameterization is particularly useful for covariate-adjusted graphical modeling. The proposed method compare favorably to existing high dimensional multivariate linear regression methodologies that are based either on minimizing non-convex criteria or certain two-step procedures. Finally, we present some theoretical properties and applications to gene network analysis.