Title
Bayesian Kernel Models: Theory and applications
Speaker
Sayan Mukherjee, Institute of Statistics and Decision Sciences, Duke University
Abstract
Kernel methods have been very popular in the machine learning literature in the last ten years, often in the context of Tikhonov regularization algorithms. I will introduce a coherent Bayesian kernel model based on an integral operator whose domain is a space of signed measures. Priors on the signed measures induce prior distributions on their image functions under the integral operator. I will identify general classes of measures whose images are dense in the reproducing kernel Hilbert space (RKHS) induced by the kernel. This gives a function-theoretic foundation for some nonparametric prior specifications commonly-used in Bayesian modeling, including Gaussian processes and Dirichlet processes, and suggests generalizations. A general framework for the construction of priors on signed measures using Lévy processes is described.
An application of this model to high-dimensional gene expression data will illustrate how this Bayesian kernel model can be used to illustrate the "when, why, and how" the incorporation of unlabelled data, semi-supervised learning, helps in predictive regression models.
This talk is based upon the following papers:
ftp.stat.duke.edu/WorkingPapers/06-18
imstat.org/sts/future_papers
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
