  The development of parsimonious models for reliable inference and prediction
of responses in high-dimensional regression settings is often challenging due
to relatively small sample sizes and the presence of complex interaction
patterns between a large number of covariates. We propose an efficient,
nonparametric framework for simultaneous variable selection, clustering and
prediction in high-throughput regression settings with continuous or discrete
outcomes, called VariScan. The VariScan model utilizes the sparsity induced by
Poisson-Dirichlet processes (PDPs) to group the covariates into
lower-dimensional latent clusters consisting of covariates with similar
patterns among the samples. The data are permitted to direct the choice of a
suitable cluster allocation scheme, choosing between PDPs and their special
case, a Dirichlet process. Subsequently, the latent clusters are used to build
a nonlinear prediction model for the responses using an adaptive mixture of
linear and nonlinear elements, thus achieving a balance between model parsimony
and flexibility. We investigate theoretical properties of the VariScan
procedure that differentiate the allocations patterns of PDPs and Dirichlet
processes both in terms of the number and relative sizes of their clusters.
Additional theoretical results guarantee the high accuracy of the model-based
clustering procedure, and establish model selection and prediction consistency.
Through simulation studies and analyses of benchmark data sets, we demonstrate
the reliability of VariScan's clustering mechanism and show that the technique
compares favorably to, and often outperforms, existing methodologies in terms
of the prediction accuracies of the subject-specific responses.
