Do Bayesian Neural Networks Need To Be Fully Stochastic?

Mrinank Sharma; Sebastian Farquhar; Eric Nalisnick; Tom Rainforth

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arXiv · 2211.06291

Do Bayesian Neural Networks Need To Be Fully Stochastic?

Mrinank Sharma·Sebastian Farquhar·Eric Nalisnick·Tom Rainforth

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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.

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Mrinank Sharma, Sebastian Farquhar, Eric Nalisnick, Tom Rainforth. 2022-11-11. Do Bayesian Neural Networks Need To Be Fully Stochastic?. https://arxiv.org/abs/2211.06291

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