DAPPr: Possibilistic Predictive Uncertainty for Deep Learning — A Lightweight Alternative to Bayesian Methods

> Paper: Possibilistic Predictive Uncertainty for Deep Learning > Authors: Yao Ni, Jeremie Houssineau, Yew Soon Ong, Piotr Koniusz > arXiv: 2605.00600 | 2026-04-30

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1. The Overconfident Deep Learning Model

Imagine a medical diagnosis AI:

• Input: a skin lesion image
• Output: "99% probability benign"
• Reality: malignant
• The model's "99% confidence" was wrong

This is the overconfidence problem in deep learning.

Models perform well on training data, but on unseen inputs they:

• Still produce high-confidence predictions
• Cannot express "I don't know"
• Become dangerous in critical applications

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2. The Dilemma of Uncertainty Quantification

Option 1: Bayesian methods

• Theoretically elegant
• Provide principled uncertainty estimates
• But computationally extremely expensive
• Require approximations (MC Dropout, variational inference)
• Nearly unusable at deep-network scale

Option 2: Second-order predictors

• Computationally efficient
• E.g., predictive variance, learned confidence
• But lack rigorous theoretical derivation
• The link between objective function and uncertainty is unclear
• Results can be unreliable

Core question: can we get both theoretical guarantees and computational efficiency?

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3. DAPPr: Dirichlet-Approximated Possibilistic Posterior Predictions

Core idea:

> Replace probability theory with possibility theory, and approximate the posterior with a Dirichlet distribution — achieving lightweight but principled uncertainty quantification.

Key distinction: probability vs. possibility

Probability:

• P(A) + P(not A) = 1
• Exact probability values must be assigned
• Bayesian updates require integration

Possibility:

• Only requires knowing "how possible" — no exact values needed
• Allows expressing "I don't know"
• Simpler update rules

DAPPr's technical approach:

1. Dirichlet approximation

• A Dirichlet distribution represents uncertainty over class probabilities
• Its parameters can be predicted directly by the network
• Computationally efficient

2. Possibilistic posterior

• Uncertainty is defined via possibility theory
• Distinguishes aleatoric uncertainty (data noise) from epistemic uncertainty (model ignorance)
• Richer semantics

3. Principled derivation

• The objective is derived from first principles
• Explicit connection between prediction objective and uncertainty quantification
• Not a heuristic trick

4. Computational efficiency

• Overhead similar to a standard classification network
• No sampling or approximate inference needed
• Scales to large models

It is a shift from "computing exact probabilities" to "estimating ranges of possibility" — faster, more flexible, yet still useful in critical decisions.

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4. Why "Possibility" May Suit Deep Learning Better Than "Probability"

The trouble with probabilistic methods:

Computational complexity:

• Bayesian inference requires integration
• Deep-network posteriors resist analytical solutions
• Approximations like MCMC are too slow

The illusion of precision:

• Even computable results are approximate
• Yet users get the impression of "exact probabilities"
• Potentially leading to misplaced trust

Advantages of the possibilistic approach:

Lightweight:

• No complex inference required
• The network directly outputs a possibility distribution
• Done in a single forward pass

Expressing ignorance:

• Probabilities must sum to 1
• Possibility allows "none of these are certain"
• Better suited to never-seen situations

Theoretical guarantees:

• A rigorous mathematical framework
• Not heuristic
• Convergence and consistency can be established

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5. A Feynman-Style Judgment: Approximation Is the Heart of Science

Feynman reportedly said:

> "An approximate answer that is good enough is better than an exact answer that is too expensive."

Applied to uncertainty quantification:

> "Bayesian probability is the gold standard, but for large-scale deep learning it is too expensive. Possibility theory offers an approximation that is 'good enough' — computationally feasible, theoretically principled, and practically effective."

DAPPr's philosophy: strike a balance between exactness and feasibility.

• Don't pretend to compute an exact Bayesian posterior (in practice, you can't)
• Instead, provide a principled approximation
• Let users know: "This is an approximation — but a reliable one"

6. Takeaways

If you're building AI systems that need uncertainty quantification, ask yourself:

1. "Is my model overconfident?" 2. "Are Bayesian methods computationally infeasible for my scenario?" 3. "Could possibility theory offer a lighter-weight alternative?" 4. "Do I need to trade off computational efficiency against theoretical guarantees?"

DAPPr reminds us: uncertainty quantification is not all-or-nothing — it's not either exact Bayesian inference or heuristic methods without guarantees. A middle ground exists, and it may be the most practical choice.

In applied deep learning, knowing "I don't know" matters as much as knowing "I know." DAPPr makes that "knowing ignorance" computationally feasible and theoretically sound.

In the ocean of uncertainty, DAPPr is a fuel-efficient lamp — it does not try to illuminate the whole ocean, only to ensure that the region it does illuminate is trustworthy.

*Forum post edited for zhichai.net. All claims reflect the linked paper as described in the original post.*