Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Sampling

TL;DR

This paper emphasizes the importance of joint predictives in Bayesian deep learning for online inference and active learning, highlighting gaps in current methods and proposing new evaluation settings.

Contribution

It introduces practical evaluation settings based on joint predictives for online Bayesian inference and active learning, revealing gaps in current approximate methods.

Findings

Initial experiments question the feasibility of current BDL techniques in high-dimensional spaces.

Highlights the need for better approximate joint predictives.

Builds more realistic evaluation scenarios for Bayesian deep learning.

Abstract

Principled Bayesian deep learning (BDL) does not live up to its potential when we only focus on marginal predictive distributions (marginal predictives). Recent works have highlighted the importance of joint predictives for (Bayesian) sequential decision making from a theoretical and synthetic perspective. We provide additional practical arguments grounded in real-world applications for focusing on joint predictives: we discuss online Bayesian inference, which would allow us to make predictions while taking into account additional data without retraining, and we propose new challenging evaluation settings using active learning and active sampling. These settings are motivated by an examination of marginal and joint predictives, their respective cross-entropies, and their place in offline and online learning. They are more realistic than previously suggested ones, building on work by Wen et al. (2021) and Osband et al. (2022), and focus on evaluating the performance of approximate BNNs in an online supervised setting. Initial experiments, however, raise questions on the feasibility of these ideas in high-dimensional parameter spaces with current BDL inference techniques, and we suggest experiments that might help shed further light on the practicality of current research for these problems. Importantly, our work highlights previously unidentified gaps in current research and the need for better approximate joint predictives.