bde: A Python Package for Bayesian Deep Ensembles via MILE

Vyron Arvanitis; Angelos Aslanidis; Emanuel Sommer; David Rügamer

cs.LGMay 13, 2026

bde: A Python Package for Bayesian Deep Ensembles via MILE

Authors: Vyron Arvanitis, Angelos Aslanidis, Emanuel Sommer, David Rügamer

Organizations: Faculty of Physics, LMU Munich, Munich, Germany · Department of Statistics, LMU Munich, Munich, Germany · 3Munich Center for Machine Learning, Munich, Germany

Abstract

bde is a user-friendly Python package for Bayesian Deep Ensembles with a particular focus on tabular data. Built on an efficient JAX implementation of the sampling-based inference method Microcanonical Langevin Ensembles (MILE), it provides scikit-learn compatible estimators for fast training, efficient Markov Chain Monte Carlo sampling, and uncertainty quantification in both regression and classification tasks.

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Apr 20, 2026 · cs.LGJ/K move · Enter open · S save

Towards E-Value Based Stopping Rules for Bayesian Deep Ensembles

Emanuel Sommer, Rickmer Schulte, Sarah Deubner, Julius Kobialka+1

LMU Munich, MCML

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.

Early Stopping Markov Chain Monte Carlo Ensemble

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Abstract

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