Title: Possibilistic Predictive Uncertainty for Deep Learning

Abstract:

While deep neural networks deliver remarkable performance across a wide array of applications, their tendency toward overconfidence when encountering unseen data highlights the critical need for robust epistemic uncertainty modeling. Current techniques for quantifying uncertainty are caught in a core conflict: Bayesian methods offer theoretically sound estimates but are often too computationally expensive to be practical, whereas more efficient second-order predictors lack a strong theoretical link between their optimization goals and the accurate measurement of epistemic uncertainty.

To address this challenge, we present Dirichlet-approximated possibilistic posterior predictions (DAPPr), a rigorous framework rooted in possibility theory. Our approach constructs a possibilistic posterior distribution over model parameters, maps this distribution into the prediction space using supremum operators, and then approximates the resulting projected posterior through learnable Dirichlet possibility functions. This projection-and-approximation methodology results in a streamlined training objective that admits closed-form solutions. Although the framework is straightforward, comprehensive experiments on various benchmarks demonstrate that DAPPr delivers uncertainty quantification performance that is either competitive with or superior to existing state-of-the-art second-order predictors. Importantly, it achieves these results while preserving theoretical rigor and computational efficiency. The source code is publicly accessible at https://github.com/MaxwellYaoNi/DAPPr.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC