Dangers of Bayesian Model Averaging under Covariate Shift

• URL: http://arxiv.org/abs/2106.11905v1
• Date: Tue, 22 Jun 2021 16:19:52 GMT
• Title: Dangers of Bayesian Model Averaging under Covariate Shift
• Authors: Pavel Izmailov, Patrick Nicholson, Sanae Lotfi, Andrew Gordon Wilson
• Abstract summary: We show how a Bayesian model average can in fact be problematic under covariate shift. We additionally show why the same issue does not affect many approximate inference procedures.
• Score: 45.20204749251884
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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