Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance, while its alternatives tend to be computationally prohibitively expensive. We tackle this challenge by revealing a previously unseen connection between inference on BNNs and volume computation problems. With this observation, we introduce a novel collapsed inference scheme that performs Bayesian model averaging using collapsed samples. It improves over a Monte-Carlo sample by limiting sampling to a subset of the network weights while pairing it with some closed-form conditional distribution over the rest. A collapsed sample represents uncountably many models drawn from the approximate posterior and thus yields higher sample efficiency. Further, we show that the marginalization of a collapsed sample can be solved analytically and efficiently despite the non-linearity of neural networks by leveraging existing volume computation solvers. Our proposed use of collapsed samples achieves a balance between scalability and accuracy. On various regression and classification tasks, our collapsed Bayesian deep learning approach demonstrates significant improvements over existing methods and sets a new state of the art in terms of uncertainty estimation as well as predictive performance.

@inproceedings{ZengBB22,
  author    = {Zeng, Zhe and Van den Broeck, Guy},
  title     = {Collapsed Inference for Bayesian Deep Learning},
  booktitle = {Proceedings of the ICML Workshop on Beyond Bayes: Paths Towards Universal Reasoning Systems},
  url       = "http://starai.cs.ucla.edu/papers/ZengBB22.pdf",
  month     = 7,
  year      = {2022},
  keywords  = {workshop}
}