Function-Space Empirical Bayes Regularisation with Student's t Priors
This addresses the problem of capturing heavy-tailed statistical characteristics in neural network outputs for researchers and practitioners in Bayesian deep learning, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackles the challenge of selecting informative prior distributions in Bayesian deep learning by proposing ST-FS-EB, a function-space empirical Bayes regularisation framework using heavy-tailed Student's t priors instead of Gaussian priors. The results demonstrate robust performance in in-distribution prediction, out-of-distribution detection, and handling distribution shifts compared to various variational inference baselines.
Bayesian deep learning (BDL) has emerged as a principled approach to produce reliable uncertainty estimates by integrating deep neural networks with Bayesian inference, and the selection of informative prior distributions remains a significant challenge. Various function-space variational inference (FSVI) regularisation methods have been presented, assigning meaningful priors over model predictions. However, these methods typically rely on a Gaussian prior, which fails to capture the heavy-tailed statistical characteristics inherent in neural network outputs. By contrast, this work proposes a novel function-space empirical Bayes regularisation framework -- termed ST-FS-EB -- which employs heavy-tailed Student's $t$ priors in both parameter and function spaces. Also, we approximate the posterior distribution through variational inference (VI), inducing an evidence lower bound (ELBO) objective based on Monte Carlo (MC) dropout. Furthermore, the proposed method is evaluated against various VI-based BDL baselines, and the results demonstrate its robust performance in in-distribution prediction, out-of-distribution (OOD) detection and handling distribution shifts.