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

Tim Pearce, Russell Tsuchida, Mohamed Zaki, Alexandra Brintrup, Andy Neely
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:134-144, 2020.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions %A Tim Pearce %A Russell Tsuchida %A Mohamed Zaki %A Alexandra Brintrup %A Andy Neely %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-pearce20a %I PMLR %P 134--144 %U https://proceedings.mlr.press/v115/pearce20a.html %V 115 %X 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.
APA
Pearce, T., Tsuchida, R., Zaki, M., Brintrup, A. & Neely, A.. (2020). Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:134-144 Available from https://proceedings.mlr.press/v115/pearce20a.html.

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