Dangers of Bayesian Model Averaging under Covariate Shift
This addresses robustness issues in Bayesian deep learning for practitioners dealing with out-of-distribution data, but it is incremental as it builds on known limitations.
The paper tackles the problem of Bayesian neural networks (BNNs) performing poorly under covariate shift, showing they can underperform classical methods due to issues with Bayesian model averaging and lack of posterior contraction. It proposes novel priors that improve BNN robustness to covariate shift.
Approximate Bayesian inference for neural networks is considered a robust alternative to standard training, often providing good performance on out-of-distribution data. However, Bayesian neural networks (BNNs) with high-fidelity approximate inference via full-batch Hamiltonian Monte Carlo achieve poor generalization under covariate shift, even underperforming classical estimation. We explain this surprising result, showing how a Bayesian model average can in fact be problematic under covariate shift, particularly in cases where linear dependencies in the input features cause a lack of posterior contraction. We additionally show why the same issue does not affect many approximate inference procedures, or classical maximum a-posteriori (MAP) training. Finally, we propose novel priors that improve the robustness of BNNs to many sources of covariate shift.