  When faced with distribution shift at test time, deep neural networks often
make inaccurate predictions with unreliable uncertainty estimates. While
improving the robustness of neural networks is one promising approach to
mitigate this issue, an appealing alternate to robustifying networks against
all possible test-time shifts is to instead directly adapt them to unlabeled
inputs from the particular distribution shift we encounter at test time.
However, this poses a challenging question: in the standard Bayesian model for
supervised learning, unlabeled inputs are conditionally independent of model
parameters when the labels are unobserved, so what can unlabeled data tell us
about the model parameters at test-time? In this paper, we derive a Bayesian
model that provides for a well-defined relationship between unlabeled inputs
under distributional shift and model parameters, and show how approximate
inference in this model can be instantiated with a simple regularized entropy
minimization procedure at test-time. We evaluate our method on a variety of
distribution shifts for image classification, including image corruptions,
natural distribution shifts, and domain adaptation settings, and show that our
method improves both accuracy and uncertainty estimation.
