Something for (almost) Nothing: Improving Deep Ensemble Calibration Using Unlabeled Data

Abstract

We present a method to improve the calibration of deep ensembles in the small training data regime in the presence of unlabeled data. Our approach is extremely simple to implement: given an unlabeled set, for each unlabeled data point, we simply fit a different randomly selected label with each ensemble member. We provide a theoretical analysis based on a PAC-Bayes bound which guarantees that if we fit such a labeling on unlabeled data, and the true labels on the training data, we obtain low negative log-likelihood and high ensemble diversity on testing samples. Crucially, each ensemble member can be trained independently from the rest (apart from the final validation/test step) making a parallel or distributed implementation extremely easy.