Robert McCulloch is a professor within the School of Mathematical and Statistical Sciences at Arizona State University. Dr. McCulloch's research focuses on Bayesian statistics. In the Bayesian approach, you write down a full joint distribution for all quantities of interest and then condition on the knowns. The computational revolution has made this strategy feasible in complex, high dimensional problems. Much of McCulloch's recent research is on Bayesian approaches for tree-based ensemble models. Tree based methods have emerged as a basic tool in Machine Learning because they are a relatively simple way to uncover complex nonlinear relationships in high dimensional problems. Ensemble methods combine many tree models into one overall model which is far more powerful than any one tree model can be on its own.
Recent applications look at personalized medicine, selection of long term portfolios (pensions), and scale conversion for Marketing data.
Talk: Multidimensional Monotonicity Discovery with mBART
Abstract: Dramatic advances in Bayesian modeling and computation have given us powerful tools for flexible fitting of high dimensional relationships. However, the flexibility and complexity of the modeling procedures comes at a price: we may have difficulty understanding what our models have found. In particular, we are often interested in finding a simple model that works well, with variable selection being an important special case. Recently Pratola et al. have developed a Bayesian approach to a model of the form Y = f(x) + s(x) Z where both the function f and s are leart using ensembles of trees. This enables us to do variable selection for the mean (f) and the volatility (s) separately. Pratola et al. using simple measures of how often a variable is used in the ensembles. In this paper we use the method of Carvlaho et al. to search for variable parsimonious approximators to the functions f and s.
Joint work with Carlos Carvalho, Hugh Chipman, Edward George, Richard Hahn, and Matthew Pratola