Tuesday, February 7th, 2012
9:30am - 10:30am, in McCormack 1-420

David Papp

Northwestern University

Polynomial optimization techniques in statistical estimation and experimental design

Abstract: Many problems in statistics can naturally be formulated as optimization models, but are usually not solved using numerical optimization methods, either because simpler closed form solutions are available, or because the natural optimization models are computationally intractable. We shall discuss two families of such problems: spline estimation with constraints on the shape of the estimator, and experimental design for regression problems. Only the simplest special cases of these problems have been solved, using ad-hoc, although often very deep, methods that cannot be generalized. The talk will present these problems from ``an optimizer's point of view''. We shall see that general versions, which include many previously unsolved cases, can be reformulated as convex conic optimization problems, using either convex programming duality or classic theorems on the representations of moments and positive polynomials. This yields a unified approach, and a single, efficient algorithm for their solution. The results will be illustrated by a few real-world examples.