Abstract

Bayesian neural networks (BNN) promise a principled approach to quantifying uncertainty in overparameterized models. Evaluating this promise is a challenge because in most practical settings, BNN predictive distributions can only be accessed through approximate inference. To systematically investigate the calibration of BNN predictive distributions, we argue for the use of discrete priors on interior parameters. We demonstrate that networks can be reverse engineered to determine which parameter ‘candidates’ should be given prior weight. This approach reveals that multimodal distributions in parameter space map to multimodal distributions in prediction space which are often only partially captured by approximate methods. We also find that uncertainty metrics have non-intuitive dependence on network dimensions, including cases where network capacity increases but uncertainty decreases. These results raise questions of whether some approximate methods may perform ‘better’ than the true BNN predictive distribution. Co-author: Youssef Marzouk