Improving predictions of Bayesian neural nets via local linearization

• URL: http://arxiv.org/abs/2008.08400v3
• Date: Thu, 25 Feb 2021 17:59:47 GMT
• Title: Improving predictions of Bayesian neural nets via local linearization
• Authors: Alexander Immer, Maciej Korzepa, Matthias Bauer
• Abstract summary: We argue that the Gauss-Newton approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN) Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation.
• Score: 79.21517734364093
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The generalized Gauss-Newton (GGN) approximation is often used to make practical Bayesian deep learning approaches scalable by replacing a second order derivative with a product of first order derivatives. In this paper we argue that the GGN approximation should be understood as a local linearization of the underlying Bayesian neural network (BNN), which turns the BNN into a generalized linear model (GLM). Because we use this linearized model for posterior inference, we should also predict using this modified model instead of the original one. We refer to this modified predictive as "GLM predictive" and show that it effectively resolves common underfitting problems of the Laplace approximation. It extends previous results in this vein to general likelihoods and has an equivalent Gaussian process formulation, which enables alternative inference schemes for BNNs in function space. We demonstrate the effectiveness of our approach on several standard classification datasets as well as on out-of-distribution detection. We provide an implementation at https://github.com/AlexImmer/BNN-predictions.

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