Adam Rothman, of the School of Statistics at the University of Minnesota, will present:

“Ideas for Multivariate Analysis in High Dimensions”

Abstract: In the first part of the talk, we develop a new method 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 be motivated through an error-in-variables formulation. We propose a non-convex weighted residual sum of squares criterion which exploits this parameterization. The optimization is solved with an accelerated proximal gradient descent algorithm. In the second part of the talk, we propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an L1 penalty on a linear function evaluated at the optimization variable corresponding to the precision matrix. We establish convergence rate bounds for these estimators and propose an alternating direction method of multipliers algorithm for their computation.

A social tea will be held at 3:00 p.m. in A434 Mayo. All are Welcome.