Posterior Uncertainty Quantification in Neural Networks using Data
  Augmentation
Luhuan Wu Sinead Williamson
In this paper, we approach the problem of uncertainty quantification in deep
learning through a predictive framework, which captures uncertainty in model
parameters by specifying our assumptions about the predictive distribution of
unseen future data. Under this view, we show that deep ensembling
(Lakshminarayanan et al., 2017) is a fundamentally mis-specified model class,
since it assumes that future data are supported on existing observations only
-- a situation rarely encountered in practice. To address this limitation, we
propose MixupMP, a method that constructs a more realistic predictive
distribution using popular data augmentation techniques. MixupMP operates as a
drop-in replacement for deep ensembles, where each ensemble member is trained
on a random simulation from this predictive distribution. Grounded in the
recently-proposed framework of Martingale posteriors (Fong et al., 2023),
MixupMP returns samples from an implicitly defined Bayesian posterior. Our
empirical analysis showcases that MixupMP achieves superior predictive
performance and uncertainty quantification on various image classification
datasets, when compared with existing Bayesian and non-Bayesian approaches.