Dr. Robert B. Gramacy (Cambridge University, currently visiting PSTAT for Fall quarter 2009)

Title: Particle Learning for Sequential Design and Optimization

Abstract: We devise a sequential Monte Carlo method, via particle learning (PL), for on-line sampling from the posterior distribution of
two static non-parametric regression models: (1) Gaussian processes (GPs), a typical choice for the sequential design of computer
experiments and optimization; and (2) a new dynamical tree model inspired by Bayesian CART. Online PL of these models, coupled with
active learning heuristics (such as the ALM/C algorithms and the expected improvement), represents a thrifty approach to sequential
design compared to MCMC which must be re-started and iterated to convergence with the inclusion of each new design point. Our
empirical results demonstrate that the PL approach yields comparable (with GPs) and better (with trees) sequential designs compared to
similar and higher-powered methods using MCMC inference, and (both) at a fraction of the computational cost. We also demonstrate how the ensemble aspects of PL lead to a better exploration of the posterior distribution compared to MCMC, which can suffer from mixing problems.

This is joint work with Nicholas Polson and Matthew Taddy, both at the University of Chicago, Booth school of business.