Possibilistic Predictive Uncertainty for Deep Learning

TL;DR

This paper introduces DAPPr, a novel possibilistic framework for epistemic uncertainty in deep learning, combining principled derivation with computational efficiency.

Contribution

It proposes a Dirichlet-approximated possibilistic posterior framework that simplifies uncertainty quantification with closed-form solutions.

Findings

Achieves competitive or superior uncertainty quantification performance.

Maintains principled derivation and computational efficiency.

Demonstrates effectiveness across diverse benchmarks.

Abstract

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modelling. Existing methods for uncertainty modelling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous derivations connecting their specific objectives to epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework leveraging possibility theory. We define a possibilistic posterior over parameters, projects this posterior to the prediction space via supremum operators, and approximates the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Extensive experiments across diverse benchmarks demonstrate that our approach achieves competitive or superior uncertainty quantification performance compared to state-of-the-art evidential deep learning methods while maintaining both principled derivation and computational efficiency. Code will be available at https://github.com/MaxwellYaoNi/DAPPr.