Papers › Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions

Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions

15 May 2019arXiv:1905.06076archive 2025-07-28

Tim Pearce, Russell Tsuchida, Mohamed Zaki, Alexandra Brintrup, Andy Neely

A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), the BNN analogue of this has not yet been explored. This paper derives BNN architectures mirroring such kernel combinations. Furthermore, it shows how BNNs can produce periodic kernels, which are often useful in this context. These ideas provide a principled approach to designing BNNs that incorporate prior knowledge about a function. We showcase the practical value of these ideas with illustrative experiments in supervised and reinforcement learning settings.

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