Positive Definite Functions, Reproducing Kernel Hilbert Spaces, and All That

• Activity Number: 576
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 4:00 PM to 5:50 PM
• Sponsor: ASA
• Author(s): Grace Wahba*+
• Companies: University of Wisconsin-Madison

Abstract

R. A. Fisher was concerned with the importance of statistical methods to scientific investigations, but could hardly have dreamed of modern methods of statistical analysis that often require modern computer capabilities unknown during his lifetime. Reproducing Kernel Hilbert spaces appeared in an influential theoretical paper (Aronszajn) in 1950, but their use as a tool in applied nonparametric regression, statistical model building and machine learning did not begin for another 20 or so years after his death. After a brief tutorial, we describe some modern manifestations of these spaces and how they are used with both simple and complex data structures.