Statistics Seminar: Distance-to-set regularization for inference under constraints

Presenter: Jason Xu, Associate Professor, Department of Biostatistics, UCLA

Description: We consider a penalty framework based on regularizing the squared distance to set-based constraints for several core statistical tasks. These distance-to-set penalties provide a simple and flexible way to cast constrained optimization problems in more tractable unconstrained forms. We will see that they often avoid drawbacks that arise from popular alternatives such as shrinkage methods. We discuss a general strategy for eliciting effective algorithms in this framework using majorization-minimization (MM), the general principle behind EM that transfers difficult problems onto a sequence of more manageable subproblems. We showcase new progress on classical problems including sparse covariance estimation using this approach, and discuss connections to Bayesian inference. In particular, analogous ideas lead to constraint relaxation and generalized profile likelihood to include optimization subproblems, leading to methods that are amenable to gradient-based posterior computation.

Bio: Jason Xu is an Associate Professor in the Department of Biostatistics at the University of California Los Angeles. Before joining the faculty at UCLA, he was a faculty member in the Department of Statistical Science at Duke University. Xu’s research program focuses on stochastic modeling and computational challenges in dynamic, dependent, and missing data settings, and he contributes tools at the interface of optimization and Bayesian approaches

Hosted by: Professor Paul Parker