# Variational Nonparametric Discriminant Analysis

## TL;DR

This paper introduces a Bayesian nonparametric discriminant analysis model that effectively performs variable selection and classification in high-dimensional data without relying on restrictive distributional assumptions.

## Contribution

It proposes a novel framework using Pólya tree priors and collapsed variational Bayes inference, enabling flexible, low-cost classification with interpretable decision rules.

## Key findings

- Performs well on simulated datasets
- Outperforms current state-of-the-art methods
- Provides interpretable decision rules

## Abstract

Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A novel Bayesian nonparametric discriminant analysis model that performs both variable selection and classification within a seamless framework is proposed. P{\'o}lya tree priors are assigned to the unknown group-conditional distributions to account for their uncertainty, and allow prior beliefs about the distributions to be incorporated simply as hyperparameters. The adoption of collapsed variational Bayes inference in combination with a chain of functional approximations led to an algorithm with low computational cost. The resultant decision rules carry heuristic interpretations and are related to an existing two-sample Bayesian nonparametric hypothesis test. By an application to some simulated and publicly available real datasets, the proposed method exhibits good performance when compared to current state-of-the-art approaches.