A Bayesian Nonparametric Perspective on Mahalanobis Distance for Out of Distribution Detection

TL;DR

This paper establishes a formal link between Bayesian nonparametric models and Mahalanobis distance for out-of-distribution detection, proposing generalized models that outperform existing methods especially with limited data or varying class covariances.

Contribution

It introduces Bayesian nonparametric mixture models with hierarchical priors that extend the Mahalanobis distance score for improved OOD detection.

Findings

Bayesian nonparametric models outperform existing OOD methods on OpenOOD benchmark.

Models are particularly effective when class covariance structures differ.

Performance gains are notable with limited data per class.

Abstract

Bayesian nonparametric methods are naturally suited to the problem of out-of-distribution (OOD) detection. However, these techniques have largely been eschewed in favor of simpler methods based on distances between pre-trained or learned embeddings of data points. Here we show a formal relationship between Bayesian nonparametric models and the relative Mahalanobis distance score (RMDS), a commonly used method for OOD detection. Building on this connection, we propose Bayesian nonparametric mixture models with hierarchical priors that generalize the RMDS. We evaluate these models on the OpenOOD detection benchmark and show that Bayesian nonparametric methods can improve upon existing OOD methods, especially in regimes where training classes differ in their covariance structure and where there are relatively few data points per class.