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Title: An explicit mean-covariance parameterization for multivariate response linear regression Authors:  Aaron Molstad - University of Florida (United States) [presenting]
Adam Rothman - University of Minnesota (United States)
Charles Doss - University of Minnesota (United States)
Guangwei Weng - University of Minnesota (United States)
Abstract: A new method is developed to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. This assumption can also be motivated through an error-in-variables formulation. Motivated by this parameterization, we propose a class of estimators that minimizes a non-convex loss plus penalty. The optimization problem is solved with an accelerated proximal gradient descent algorithm. We show our method can outperform competitors in both real and simulated data examples.