Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions
Tim Pearce, Russell Tsuchida, Mohamed Zaki, Alexandra Brintrup, Andy Neely
Abstract
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.
BibTeX
@InProceedings{pmlr-v115-pearce20a,
title = {Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions},
author = {Pearce, Tim and Tsuchida, Russell and Zaki, Mohamed and Brintrup, Alexandra and Neely, Andy},
booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference},
pages = {134--144},
year = {2020},
editor = {Adams, Ryan P. and Gogate, Vibhav},
volume = {115},
series = {Proceedings of Machine Learning Research},
month = {22--25 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v115/pearce20a/pearce20a.pdf},
url = {https://proceedings.mlr.press/v115/pearce20a.html},
abstract = {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.}
}