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When faced with distribution shift at test time, deep neural networks oftenmake inaccurate predictions with unreliable uncertainty estimates. Whileimproving the robustness of neural networks is one promising approach tomitigate this issue, an appealing alternate to robustifying networks againstall possible test-time shifts is to instead directly adapt them to unlabeledinputs from the particular distribution shift we encounter at test time.However, this poses a challenging question: in the standard Bayesian model forsupervised learning, unlabeled inputs are conditionally independent of modelparameters when the labels are unobserved, so what can unlabeled data tell usabout the model parameters at test-time? In this paper, we derive a Bayesianmodel that provides for a well-defined relationship between unlabeled inputsunder distributional shift and model parameters, and show how approximateinference in this model can be instantiated with a simple regularized entropyminimization procedure at test-time. We evaluate our method on a variety ofdistribution shifts for image classification, including image corruptions,natural distribution shifts, and domain adaptation settings, and show that ourmethod improves both accuracy and uncertainty estimation.

Training on Test Data with Bayesian Adaptation for Covariate Shift