Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study

TL;DR

This study compares set-based and distribution-based epistemic uncertainty representations in neural networks, using a controlled, like-for-like evaluation across multiple benchmarks to clarify their relative strengths and practical implications.

Contribution

It provides the first controlled, direct comparison of the two paradigms using identical predictive distributions, isolating their effects on uncertainty estimation performance.

Findings

Distribution-based methods generally outperform set-based methods in uncertainty tasks.

The choice of representation significantly impacts out-of-distribution detection accuracy.

Both frameworks can be meaningfully compared, revealing their respective advantages and limitations.

Abstract

Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex sets of probability distributions). These frameworks are often regarded as fundamentally non-comparable due to differing semantics, assumptions, and evaluation practices, leaving their relative merits unclear. Empirical comparisons are further confounded by variations in the underlying predictive models. To clarify this issue, we present a controlled comparative study enabling principled, like-for-like evaluation of the two paradigms. Both representations are constructed from the same finite collection of predictive distributions generated by a shared neural network, isolating representational effects from predictive accuracy. Our study evaluates each representation through the lens of 3 uncertainty measures across 8 benchmarks, including selective prediction and out-of-distribution detection, spanning 6 underlying predictive models and 10 independent runs per configuration. Our results show that meaningful comparison between these seemingly non-comparable frameworks is both feasible and informative, providing insights into how second-order representation choices impact practical uncertainty-aware performance.