Dr. Alvaro Nosedal-Sanchez of the Mathematics Department will give a colloquium entitled “Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial.”

The colloquium will be on Wednesday, April 27, 2011, at 3:30 p.m. in Stright Hall, Room 202.

## Abstract

Penalized Regression procedures have become very popular ways to estimate complex functions. The smoothing spline, for example, is the solution of a minimization problem in a functional space. If such a minimization problem is posed on a reproducing kernel Hilbert space (RKHS), the solution is guaranteed to exist, is unique, and has a very simple form. There are excellent books and articles about RKHS and their applications in statistics; however, this existing literature is very dense. Our intention is to provide a friendly reference for someone approaching this subject for the first time.

This talk begins with a simple problem, a system of linear equations, then gives an intuitive motivation for reproducing kernels. Armed with the intuition gained from our first examples, we take the reader from Vector Spaces to Banach Spaces and to RKHS. Finally, we present some statistical estimation problems that can be solved using the mathematical machinery discussed.