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The goal of this presentation is to build an efficient non-parametric Bayesclassifier in the presence of large numbers of predictors. When analyzing suchdata, parametric models are often too inflexible while non-parametricprocedures tend to be non-robust because of insufficient data on these highdimensional spaces. When dealing with these types of data, it is often the casethat most of the variability tends to lie along a few directions, or moregenerally along a much smaller dimensional subspace of the feature space. Hencea class of regression models is proposed that flexibly learn about thissubspace while simultaneously performing dimension reduction in classification.This methodology, allows the cell probabilities to vary non-parametricallybased on a few coordinates expressed as linear combinations of the predictors.Also, as opposed to many black-box methods for dimensionality reduction, theproposed model is appealing in having clearly interpretable and identifiableparameters which provide insight into which predictors are important indetermining accurate classification boundaries. Gibbs sampling methods aredeveloped for posterior computations. The estimated cell probabilities aretheoretically shown to be consistent, and real data applications are includedto support the findings.

Nonparametric Bayes Classification via Learning of Affine Subspaces