Adaptive Priors from Learning Trajectories for Function-Space Bayesian Neural Networks

Yohan Jung, Juho Lee

Keywords: Function-space Bayesian neural network, Function-space variational inference, Gaussian process, Stochastic weight averaging gaussian (SWAG))

TL;DR: Some equations, simple statement and proof, and experiment demonstrating the statement

Abstract:

Tractable Function-space Variational Inference (T-FVI) provides a way to estimate the function-space Kullback-Leibler (KL) divergence between a random prior function and its posterior. This allows the optimization of the function-space KL divergence via Stochastic Gradient Descent (SGD) and thus simplifies the training of function-space Bayesian Neural Networks (BNNs). However, function-space BNNs on high-dimensional datasets typically require deep neural networks (DNN) with numerous parameters, and thus defining suitable function-space priors remains challenging. For instance, the Gaussian Process (GP) prior suffers from scalability issues, and DNNs do not provide a clear way to set appropriate weight parameters to achieve meaningful function-space priors. To address this issue, we propose an explicit form of function-space priors that can be easily integrated into widely-used DNN architectures, while adaptively incorporating different levels of uncertainty based on the function's inputs. To achieve this, we consider DNNs as Bayesian last-layer models to
obtain the explicit mean and variance functions of our prior. The parameters of these explicit functions are determined using the weight statistics over the learning trajectory. Our empirical experiments show improved uncertainty estimation in image classification, transfer learning, and UCI regression tasks.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 4147