Data augmentation in Bayesian neural networks and the cold posterior effect
This addresses the issue of interpreting Bayesian methods in deep learning for researchers, but it is incremental as it builds on prior work to refine understanding.
The paper tackles the problem of principled Bayesian neural networks with data augmentation, showing that the cold posterior effect persists even in these models, suggesting it is not an artifact of incorrect likelihoods.
Bayesian neural networks that incorporate data augmentation implicitly use a ``randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function'' (Izmailov et al. 2021). Here, we provide several approaches to developing principled Bayesian neural networks incorporating data augmentation. We introduce a ``finite orbit'' setting which allows likelihoods to be computed exactly, and give tight multi-sample bounds in the more usual ``full orbit'' setting. These models cast light on the origin of the cold posterior effect. In particular, we find that the cold posterior effect persists even in these principled models incorporating data augmentation. This suggests that the cold posterior effect cannot be dismissed as an artifact of data augmentation using incorrect likelihoods.