Chapters
Abstract:
It is routine in many fields to collect data having a variety of measurement scales and supports. For example, in biomedical studies for each patient one may collect functional data on a biomarker over time, gene expression values normalized to lie on a hypersphere to remove artifacts, clinical and demographic covariates and a health outcome. A common interest focuses on building predictive models, with parametric assumptions seldom supported by prior knowledge. Hence, it is most appropriate to define a prior with large support allowing the conditional distribution of the response given predictors to be unknown and changing flexibly across the predictor space not just in the mean but also in the variance and shape. Building on earlier work on Dirichlet process mixtures, we describe a simple and general strategy for inducing models for conditional distributions through discrete mixtures of product kernel models for joint distributions of predictors and response variables. Computation is straightforward and the approach can easily accommodate combining of widely disparate data types, including vector data in a Euclidean space, categorical observations, functions, images and manifold data.