Possibilistic Predictive Uncertainty for Deep Learning

• URL: http://arxiv.org/abs/2605.00600v1
• Date: Fri, 01 May 2026 12:14:01 GMT
• Title: Possibilistic Predictive Uncertainty for Deep Learning
• Abstract summary: We introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr)<n>DAPPr is a principled framework leveraging possibility theory.<n>This projection-and-approximation strategy yields a simple training objective with closed-form solutions.
• Score: 75.00607359322863
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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