Possibilistic Predictive Uncertainty for Deep Learning

2026-06-12 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

Dirichlet-approximated possibilistic posterior predictions (DAPPr) is a new framework for deep learning that addresses the dilemma of reliable epistemic uncertainty modeling. It leverages possibility theory to provide principled uncertainty estimates while maintaining computational efficiency. DAPPr defines a possibilistic posterior over parameters, projects it to the prediction space using supremum operators, and approximates it with learnable Dirichlet possibility functions. This strategy results in a simple training objective with closed-form solutions. Extensive experiments across diverse benchmarks, including MNIST, CIFAR-10/100, CIFAR-10-LT, and fine-grained datasets, demonstrate that DAPPr achieves competitive or superior uncertainty quantification compared to state-of-the-art evidential deep learning methods. Its code will be available at https://github.com/MaxwellYaoNi/DAPPr.

Key takeaway

For AI Scientists and Machine Learning Engineers building high-stakes deep learning applications, DAPPr offers a robust solution for epistemic uncertainty. You should consider integrating DAPPr into your models, especially if current Bayesian methods are too slow or evidential deep learning approaches lack theoretical rigor. Its principled derivation and computational efficiency provide more reliable uncertainty estimates, crucial for safe deployment in areas like autonomous driving or medical diagnosis.

Key insights

DAPPr uses possibility theory for principled, computationally efficient epistemic uncertainty quantification in deep learning.

Principles

• Possibility theory offers tractable epistemic uncertainty modeling.
• Projecting parameter posteriors to prediction space simplifies objectives.
• Approximating with Dirichlet possibility functions yields closed-form solutions.

Method

DAPPr defines a possibilistic posterior over parameters, projects it to the prediction space via supremum operators, and approximates it using learnable Dirichlet possibility functions, yielding a simple training objective with closed-form solutions.

In practice

• Replace standard cross-entropy loss with "DAPPr_loss" in PyTorch.
• Derive Dirichlet parameters "alpha" using "softplus(logits) + 1".
• Apply a spurious evidence regularizer to prevent unbounded precision.

Topics

• Epistemic Uncertainty
• Possibility Theory
• Deep Learning
• Dirichlet Distributions
• Uncertainty Quantification
• Evidential Deep Learning

Code references

• MaxwellYaoNi/DAPPr

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.