From Partial Exchangeability to Predictive Probability: A Bayesian Perspective on Classification

TL;DR

This paper introduces a new Bayesian nonparametric classification model that integrates Gaussian process and Dirichlet process priors, enhancing flexibility in uncertainty modeling and outperforming standard logistic regression in simulations.

Contribution

It presents a novel Bayesian classification framework combining Gaussian and Dirichlet processes, extending de Finetti's theorem for improved uncertainty modeling.

Findings

Outperforms standard logistic regression in simulated data

Provides flexible uncertainty modeling in classification

Extends theoretical framework of de Finetti representation

Abstract

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti representation theorem and the construction of random distribution functions made by Ferguson (1973). This approach allows for flexible uncertainty modeling in both the latent score and the mapping to probabilities. We demonstrate the method performance using simulated data where it outperforms standard logistic regression.