Statistical learning: models and algorithms

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Statistical scientists are being challenged to invent sophisticated models as a tool for discovery in problems with richly structured data. My research will attempt to bring core statistical ideas, such as accurate assessment of uncertainty, sequential design of experiments, mixed and mixture models, to bear on these challenging problems. Bayesian statistical methods will often be used, for their capacity to flexibly represent uncertainty and compute estimates using all available data. This long-term vision will be realized via work in three areas: I will generalize my earlier results on Bayesian ensemble models, which seek to build predictive (regression) models out of a collection of simpler models, such as trees. Generalizations will include variable selection, more flexible error distributions, and the coupling of sequential design strategies with flexible ensemble models in traditional and computer experiments. The second area will involve modelling of network data, such as email transactions. By developing probabilistic models that allow emailers to belong to groups, a probabilistic analogue of clustering can be accomplished. This first step in network modelling will form the basis for time-varying models. The third area will involve unsupervised learning (also known as clustering), attacked from the viewpoint of mixture models. Mixture models provide a flexible way of modelling additional heterogeneity in data. Such heterogeneity can enter into a predictive model as a "random effect", flexibly describing heterogeneity. Developments will include (i) mixtures in functional data as a way of characterizing variation and forming a basis for process monitoring (ii) classification via modelling of within-class covariate distributions as mixtures, and the network model described above. By bringing together ideas from Machine Learning and Statistics, the impact of my work will be to enrich both disciplines, stimulate research in modelling of new and richly structured data, and provide highly qualified personnel the training necessary to work at the frontier of these two domains.