  We introduce a new nonlinear model for classification, in which we model the
joint distribution of response variable, y, and covariates, x,
non-parametrically using Dirichlet process mixtures. We keep the relationship
between y and x linear within each component of the mixture. The overall
relationship becomes nonlinear if the mixture contains more than one component.
We use simulated data to compare the performance of this new approach to a
simple multinomial logit (MNL) model, an MNL model with quadratic terms, and a
decision tree model. We also evaluate our approach on a protein fold
classification problem, and find that our model provides substantial
improvement over previous methods, which were based on Neural Networks (NN) and
Support Vector Machines (SVM). Folding classes of protein have a hierarchical
structure. We extend our method to classification problems where a class
hierarchy is available. We find that using the prior information regarding the
hierarchical structure of protein folds can result in higher predictive
accuracy.
