Nonlinear Models Using Dirichlet Process Mixtures

Babak Shahbaba, Dept. of Public Health Sciences, University of Toronto
Radford M. Neal, Dept. of Statistics and Dept. of Computer Science, University of Toronto

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.

Technical Report No. 0707, Dept. of Statistics, University of Toronto (March 2007), 16 pages: postscript, pdf.

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A substantially revised version appeared as the following paper:

Shahbaba, B. and Neal, R. M. (2009) ``Nonlinear Models Using Dirichlet Process Mixtures'', Journal of Machine Learning Research, vol. 10, pp. 1829-1850: abstract, pdf.