The Gaussian Radon transform for Banach spaces and machine learning

Stochastics Seminar
Thursday, April 10, 2014 - 15:05
1 hour (actually 50 minutes)
Skiles 005
Louisiana State University
In this talk we investigate possible applications of the infinitedimensional Gaussian Radon transform for Banach spaces to machine learning. Specifically, we show that the Gaussian Radon transform offers a valid stochastic interpretation to the ridge regression problem in the case when the reproducing kernel Hilbert space in question is infinite-dimensional. The main idea is to work with stochastic processes defined not on the Hilbert space itself, but on the abstract Wiener space obtained by completing the Hilbert space with respect to a measurable norm.