Robust PAC$^m$: Training Ensemble Models Under Misspecification and Outliers

TL;DR

This paper introduces a robust free energy criterion based on PAC$^m$ bounds that improves ensemble model training by effectively handling model misspecification and outliers, enhancing generalization.

Contribution

It proposes a novel robust free energy training criterion combining generalized logarithm scores with PAC$^m$ bounds, addressing limitations of Bayesian learning under misspecification and outliers.

Findings

Enhanced ensemble predictor performance under misspecification.

Robust predictive distributions counteracting outliers.

Theoretical validation of the new free energy criterion.

Abstract

Standard Bayesian learning is known to have suboptimal generalization capabilities under misspecification and in the presence of outliers. PAC-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a bound on the generalization error for Gibbs predictors (i.e., for single models drawn at random from the posterior) under the assumption of sampling distributions uncontaminated by outliers. This viewpoint provides a justification for the limitations of Bayesian learning when the model is misspecified, requiring ensembling, and when data is affected by outliers. In recent work, PAC-Bayes bounds -- referred to as PAC$^m$ -- were derived to introduce free energy metrics that account for the performance of ensemble predictors, obtaining enhanced performance under misspecification. This work presents a novel robust free energy criterion that combines the generalized logarithm score function with PAC$^m$ ensemble bounds. The proposed free energy training criterion produces predictive distributions that are able to concurrently counteract the detrimental effects of misspecification -- with respect to both likelihood and prior distribution -- and outliers.