Statistical methods often involve solving an optimization problem, such as in maximum likelihood estimation and regression. The addition of constraints, either to enforce a hard requirement in estimation or to regularize solutions, complicates matters. Fortunately, the rich theory of convex optimization provides ample tools for devising novel methods. In this talk, I present applications of distance-to-set penalties to statistical learning problems. Specifically, I will focus on proximal distance algorithms, based on the MM principle, tailored to various applications such as regression and discriminant analysis. Special emphasis is given to sparsity set constraints as a compromise between exhaustive combinatorial searches and lasso penalization methods that induce shrinkage.

Dr. Alfonso Landeros