GSO Spring Speaker 2012

Bayesian Nonparametric Models Using Lévy Random Fields and Overcomplete Dictionaries

Merlise Clyde
Professor
Department of Statistical Science, Duke University

Venue: SC239

Abstract:

Lévy random fields, although less well known than Gaussian random fields, are ideally suited for constructing nonparametric prior distributions on unknown functions using expansions with overcomplete, and in particular, continuous dictionaries. In this talk I will provide an overview of constructing nonparametric priors distributions on functions using Lévy random fields and how these relate to the more familiar compound Poisson process and limits of other finite dimensional expansions, in particular kernel regression and support vector machines. Under suitable conditions on hyperparameters, the resulting functions are able to adapt to unknown smoothness and sparsity similar to wavelet models. In fact stochastic expansions using continuous wavelet dictionaries may be viewed as a special case. I'll review key theoretical results and provide practical details about computational implementation. Finally, I'll illustrate the methodology using MALDI-TOF mass spectroscopy data, air pollution fields (space and/or time), and other classification problems from machine learning and close with open problems.