Function-Space Empirical Bayes Regularisation with Student's t Priors

Fuente: arXiv
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Main Authors: Hao, Pengcheng, Kuruoglu, Ercan Engin
Format: Preprint
Published: 2026
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author Hao, Pengcheng
Kuruoglu, Ercan Engin
author_facet Hao, Pengcheng
Kuruoglu, Ercan Engin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2602_22015
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Function-Space Empirical Bayes Regularisation with Student's t Priors
Hao, Pengcheng
Kuruoglu, Ercan Engin
Machine Learning
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.
title Function-Space Empirical Bayes Regularisation with Student's t Priors
topic Machine Learning
url https://arxiv.org/abs/2602.22015