Nonlinear Models Using Dirichlet Process Mixtures

TL;DR

This paper presents a novel nonlinear classification model using Dirichlet process mixtures that adaptively captures complex relationships, outperforming traditional models like neural networks and SVMs, especially in hierarchical protein fold classification.

Contribution

The paper introduces a nonparametric Dirichlet process mixture model for nonlinear classification, extending it to hierarchical classes for improved accuracy.

Findings

Model outperforms multinomial logit, quadratic MNL, decision trees, neural networks, and SVMs.

Incorporating hierarchical class information improves predictive accuracy.

Model effectively captures complex nonlinear relationships in data.

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. We find that using the prior information regarding the hierarchical structure of protein folds can result in higher predictive accuracy.