Dangers of Bayesian Model Averaging under Covariate Shift

Pavel Izmailov, Patrick Nicholson, Sanae Lotfi, Andrew Gordon Wilson

Keywords: Bayesian, Bayesian neural networks, neural networks, covariate shift, out-of-distribution generalization

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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TL;DR: We demonstrate, explain, and remedy poor performance of Bayesian neural networks under covariate shift.

Code: https://github.com/izmailovpavel/bnn_covariate_shift

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2106.11905/code)