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Abstract:
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.