Do Bayesian Neural Networks Need To Be Fully Stochastic?

Mrinank Sharma, Sebastian Farquhar, Eric Nalisnick, Tom Rainforth
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:7694-7722, 2023.

Abstract

We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that expressive predictive distributions require only small amounts of stochasticity. In particular, partially stochastic networks with only n stochastic biases are universal probabilistic predictors for n-dimensional predictive problems. In empirical investigations, we find no systematic benefit of full stochasticity across four different inference modalities and eight datasets; partially stochastic networks can match and sometimes even outperform fully stochastic networks, despite their reduced memory costs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-sharma23a, title = {Do Bayesian Neural Networks Need To Be Fully Stochastic?}, author = {Sharma, Mrinank and Farquhar, Sebastian and Nalisnick, Eric and Rainforth, Tom}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {7694--7722}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/sharma23a/sharma23a.pdf}, url = {https://proceedings.mlr.press/v206/sharma23a.html}, abstract = {We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that expressive predictive distributions require only small amounts of stochasticity. In particular, partially stochastic networks with only n stochastic biases are universal probabilistic predictors for n-dimensional predictive problems. In empirical investigations, we find no systematic benefit of full stochasticity across four different inference modalities and eight datasets; partially stochastic networks can match and sometimes even outperform fully stochastic networks, despite their reduced memory costs.} }
Endnote
%0 Conference Paper %T Do Bayesian Neural Networks Need To Be Fully Stochastic? %A Mrinank Sharma %A Sebastian Farquhar %A Eric Nalisnick %A Tom Rainforth %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-sharma23a %I PMLR %P 7694--7722 %U https://proceedings.mlr.press/v206/sharma23a.html %V 206 %X We investigate the benefit of treating all the parameters in a Bayesian neural network stochastically and find compelling theoretical and empirical evidence that this standard construction may be unnecessary. To this end, we prove that expressive predictive distributions require only small amounts of stochasticity. In particular, partially stochastic networks with only n stochastic biases are universal probabilistic predictors for n-dimensional predictive problems. In empirical investigations, we find no systematic benefit of full stochasticity across four different inference modalities and eight datasets; partially stochastic networks can match and sometimes even outperform fully stochastic networks, despite their reduced memory costs.
APA
Sharma, M., Farquhar, S., Nalisnick, E. & Rainforth, T.. (2023). Do Bayesian Neural Networks Need To Be Fully Stochastic?. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:7694-7722 Available from https://proceedings.mlr.press/v206/sharma23a.html.

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