Laplace Redux -- Effortless Bayesian Deep Learning

TL;DR

This paper advocates for the Laplace approximation in Bayesian deep learning, demonstrating its simplicity, efficiency, and competitive performance compared to other methods, supported by a new software library and extensive experiments.

Contribution

The paper introduces 'laplace', a user-friendly PyTorch library for all major Laplace approximation variants, and shows through experiments that LA is cost-effective and competitive with popular Bayesian methods.

Findings

Laplace approximation is computationally efficient and competitive in performance.

The 'laplace' library simplifies implementation of LA in PyTorch.

LA can be effectively used in domains where Bayesian deep learning is not common.

Abstract

Bayesian formulations of deep learning have been shown to have compelling theoretical properties and offer practical functional benefits, such as improved predictive uncertainty quantification and model selection. The Laplace approximation (LA) is a classic, and arguably the simplest family of approximations for the intractable posteriors of deep neural networks. Yet, despite its simplicity, the LA is not as popular as alternatives like variational Bayes or deep ensembles. This may be due to assumptions that the LA is expensive due to the involved Hessian computation, that it is difficult to implement, or that it yields inferior results. In this work we show that these are misconceptions: we (i) review the range of variants of the LA including versions with minimal cost overhead; (ii) introduce "laplace", an easy-to-use software library for PyTorch offering user-friendly access to all major flavors of the LA; and (iii) demonstrate through extensive experiments that the LA is competitive with more popular alternatives in terms of performance, while excelling in terms of computational cost. We hope that this work will serve as a catalyst to a wider adoption of the LA in practical deep learning, including in domains where Bayesian approaches are not typically considered at the moment.