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.

Bayesian deep learning has always garnered substantial interest in the machine learning community.

This paper presents an innovative approach to classification tasks called Credal Deep Ensembles (CreDEs), ensembles of novel Credal-Set Neural Networks (CreNets), aiming to improve EU quantification in the framework of credal inference.

We compare the algorithms on a wide range of large, convolutional and transformer-based neural network architectures.

Neural networks are known toproduce poor uncertainty estimations, and avariety of approaches have been proposed to remedy this issue.

Although the ongoing success of deep learning is remarkable, the increasing data, model and training algorithm complexity makeathorough understanding oftheir inner workings increasingly difficult.

This is the appendix of the paper " Quantification of Uncertainty with Adversarial Models ". It consists of three sections.