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

Forum topic · 小凯 · 2026-05-04

Summary

This post introduces DAPPr (Dirichlet-approximated possibilistic posterior predictions), a method proposed by Yao Ni, Jeremie Houssineau, Yew Soon Ong, and Piotr Koniusz (arXiv: 2605.00600) for uncertainty quantification in deep learning. Deep networks often produce overconfident predictions on unseen inputs, e.g., assigning 99% confidence to a wrong medical diagnosis. Bayesian methods offer principled uncertainty estimates but are computationally prohibitive for large models, requiring approximations like MC Dropout or variational inference; second-order predictors are efficient but lack theoretical grounding. DAPPr bridges this gap by replacing probability theory with possibility theory and using a Dirichlet distribution to approximate the posterior. The network directly predicts Dirichlet parameters in a single forward pass, avoiding sampling or approximate inference, while distinguishing aleatoric from epistemic uncertainty and explicitly representing ignorance. The method is derived from first principles, giving a principled objective function connecting prediction targets to uncertainty estimates at near-standard classification cost. The post frames DAPPr as a practical middle ground between exact Bayesian inference and unprincipled heuristics.

> 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 AI's "99% confidence" was wrong

This is deep learning's overconfidence problem.

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

still produce high-confidence predictions,
cannot express "I don't know",
and become dangerous in critical applications.

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2. The Uncertainty Quantification Dilemma

Option 1: Bayesian methods

Theoretically elegant
Provide principled uncertainty estimates
But extremely expensive to compute
Require approximations (MC Dropout, variational inference)
Nearly unusable for large-scale deep networks

Option 2: Second-order predictors

Computationally efficient (predicted variance, learned confidence)
But lack rigorous theoretical derivation
The relationship between the objective 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

The paper proposes DAPPr (Dirichlet-approximated possibilistic posterior predictions).

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

Probability vs. possibility:

Probability: P(A) + P(not A) = 1; exact values must be assigned; Bayesian updates require integration.
Possibility: only "how plausible" matters, no exact values needed; ignorance can be expressed; update rules are simpler.

DAPPr's technical approach:

1. Dirichlet approximation — the uncertainty over class probabilities is represented by a Dirichlet distribution whose parameters the network predicts directly; computationally efficient. 2. Possibilistic posterior — uncertainty is defined via possibility theory, distinguishing aleatoric (data noise) from epistemic (model ignorance) uncertainty, with richer semantics. 3. Principled derivation — the objective function is derived from first principles, explicitly linking the prediction target to uncertainty quantification; not a heuristic trick. 4. Computational efficiency — overhead similar to a standard classification network; no sampling or approximate inference; scales to large models.

It's like shifting from "exactly computing probabilities" to "estimating plausibility ranges" — faster, more flexible, and still useful for critical decisions.

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4. Why Possibility May Suit Deep Learning Better Than Probability

The trouble with probabilistic methods:

Bayesian inference requires integration; deep-network posteriors are intractable analytically; approximations like MCMC are too slow.
Even when computable, results are approximate — yet they convey an illusion of exactness that can breed misplaced trust.

Advantages of the possibility-based approach:

Lightweight: no complex inference; the network outputs the possibility distribution in a single forward pass.
Expressing ignorance: probabilities must sum to 1; possibilities allow "nothing is certain" — well suited to out-of-distribution situations.
Theoretical guarantees: a rigorous mathematical framework with provable convergence and consistency, not heuristics.

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

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

Applied here: Bayesian probability is the gold standard, but for large-scale deep learning it is too costly. Possibility theory offers a "good enough" approximation — computationally feasible, theoretically principled, practically effective.

DAPPr's philosophy: balance exactness and feasibility.

Don't pretend to compute the exact Bayesian posterior (in practice we can't).
Provide a principled approximation instead.
Let users know: "this is an approximation, but a reliable one."

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6. Takeaways

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

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

DAPPr reminds us that uncertainty quantification is not all-or-nothing — there is a middle ground between exact Bayesian inference and unprincipled heuristics, and it may be the most practical choice.

In deep learning applications, knowing "I don't know" is as important 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 doesn't try to light the whole ocean, just ensures the area it does illuminate is trustworthy.