Possibilistic Predictive Uncertainty for Deep Learning

Yao Ni, Jeremie Houssineau, Yew-Soon Ong, Piotr Koniusz
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:92925-92944, 2026.

Abstract

Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-ni26b, title = {Possibilistic Predictive Uncertainty for Deep Learning}, author = {Ni, Yao and Houssineau, Jeremie and Ong, Yew-Soon and Koniusz, Piotr}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {92925--92944}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/ni26b/ni26b.pdf}, url = {https://proceedings.mlr.press/v306/ni26b.html}, abstract = {Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency.} }
Endnote
%0 Conference Paper %T Possibilistic Predictive Uncertainty for Deep Learning %A Yao Ni %A Jeremie Houssineau %A Yew-Soon Ong %A Piotr Koniusz %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-ni26b %I PMLR %P 92925--92944 %U https://proceedings.mlr.press/v306/ni26b.html %V 306 %X Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency.
APA
Ni, Y., Houssineau, J., Ong, Y. & Koniusz, P.. (2026). Possibilistic Predictive Uncertainty for Deep Learning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:92925-92944 Available from https://proceedings.mlr.press/v306/ni26b.html.

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