CIS Project 22359, Final Technical Report. Discretized Posterior Approximation in High Dimensions

Abstract

Our primary aim in this work is to understand how to efficiently obtain reliable uncertainty quantification in automatic learning algorithms with limited training datasets. Standard approaches rely on cross-validation to tune hyper parameters. Unfortunately, when our datasets are too small, holdout datasets become unreliable—albeit unbiased—measures of prediction quality due to the lack of adequate sample size. We should not place confidence in holdout estimators under conditions wherein the sample variance is both large and unknown. More poigniantly, our training experiments on limited data (Duersch and Catanach, 2021) show that even if we could improve estimator quality under these conditions, the typical training trajectory may never even encounter generalizable models.