Robust PAC$^m$: Training Ensemble Models Under Misspecification and Outliers
This work addresses limitations in Bayesian learning for practitioners dealing with imperfect models and noisy data, representing an incremental improvement over prior PAC^m methods.
The paper tackles the problem of Bayesian learning's suboptimal generalization under model misspecification and outliers by proposing a robust free energy criterion that combines a generalized logarithm score with PAC^m ensemble bounds, resulting in predictive distributions that counteract both misspecification and outlier effects.
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.