Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Sommer, Emanuel, Schulte, Rickmer, Deubner, Sarah, Kobialka, Julius, Rügamer, David
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918456694145024
author Sommer, Emanuel
Schulte, Rickmer
Deubner, Sarah
Kobialka, Julius
Rügamer, David
author_facet Sommer, Emanuel
Schulte, Rickmer
Deubner, Sarah
Kobialka, Julius
Rügamer, David
contents Bayesian Deep Ensembles (BDEs) represent a powerful approach for uncertainty quantification in deep learning, combining the robustness of Deep Ensembles (DEs) with flexible multi-chain MCMC. While DEs are affordable in most deep learning settings, (long) sampling of Bayesian neural networks can be prohibitively costly. Yet, adding sampling after optimizing the DEs has been shown to yield significant improvements. This leaves a critical practical question: How long should the sequential sampling process continue to yield significant improvements over the initial optimized DE baseline? To tackle this question, we propose a stopping rule based on E-values. We formulate the ensemble construction as a sequential anytime-valid hypothesis test, providing a principled way to decide whether or not to reject the null hypothesis that MCMC offers no improvement over a strong baseline, to early stop the sampling. Empirically, we study this approach for diverse settings. Our results demonstrate the efficacy of our approach and reveal that only a fraction of the full-chain budget is often required.
format Preprint
id arxiv_https___arxiv_org_abs_2604_18089
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles
Sommer, Emanuel
Schulte, Rickmer
Deubner, Sarah
Kobialka, Julius
Rügamer, David
Machine Learning
Bayesian Deep Ensembles (BDEs) represent a powerful approach for uncertainty quantification in deep learning, combining the robustness of Deep Ensembles (DEs) with flexible multi-chain MCMC. While DEs are affordable in most deep learning settings, (long) sampling of Bayesian neural networks can be prohibitively costly. Yet, adding sampling after optimizing the DEs has been shown to yield significant improvements. This leaves a critical practical question: How long should the sequential sampling process continue to yield significant improvements over the initial optimized DE baseline? To tackle this question, we propose a stopping rule based on E-values. We formulate the ensemble construction as a sequential anytime-valid hypothesis test, providing a principled way to decide whether or not to reject the null hypothesis that MCMC offers no improvement over a strong baseline, to early stop the sampling. Empirically, we study this approach for diverse settings. Our results demonstrate the efficacy of our approach and reveal that only a fraction of the full-chain budget is often required.
title Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles
topic Machine Learning
url https://arxiv.org/abs/2604.18089