Learning phenotype densities conditional on many interacting predictors

MOTIVATION: Estimating a phenotype distribution conditional on a set of discrete-valued predictors is a commonly encountered task. For example, interest may be in how the density of a quantitative trait varies with single nucleotide polymorphisms and patient characteristics. The subset of important predictors is not usually known in advance. This becomes more challenging with a high-dimensional predictor set when there is the possibility of interaction. RESULTS: We demonstrate a novel non-parametric Bayes method based on a tensor factorization of predictor-dependent weights for Gaussian kernels. The method uses multistage predictor selection for dimension reduction, providing succinct models for the phenotype distribution. The resulting conditional density morphs flexibly with the selected predictors. In a simulation study and an application to molecular epidemiology data, we demonstrate advantages over commonly used methods.