# Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles

arXiv: https://arxiv.org/abs/2604.18089 · HTML: https://mlsanity.com/paper/2604.18089/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Sampling from Bayesian Neural Network Posteriors with Symmetric Minibatch Splitting Langevin Dynamics](https://mlsanity.com/paper/2410.19780/) (2024)
- [Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?](https://mlsanity.com/paper/2602.06500/) (2026)

## Built on by (most cited first, 2 of 2)

- [Position: The Time for Sampling Is Now! Charting a New Course for Bayesian Deep Learning](https://mlsanity.com/paper/2605.21765/) (2026)
- [ScoreStop: Gradient-based early stopping using functional score tests](https://mlsanity.com/paper/2606.02740/) (2026)

## Abstract (arXiv)

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.