Optimal Conformal Prediction under Epistemic Uncertainty

2026-07-09 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This paper introduces Bernoulli Prediction Sets (BPS), a novel conformal prediction method designed for classification tasks that explicitly addresses epistemic uncertainty. Unlike standard conformal prediction, which relies on first-order probabilistic predictors, BPS integrates second-order predictors such as credal sets or Bayesian models. BPS constructs the smallest possible prediction sets that guarantee conditional coverage of the true label, assuming valid second-order predictions. When given first-order predictions, BPS simplifies to the well-known Adaptive Prediction Sets (APS). For scenarios where the validity assumption of second-order predictions is compromised, BPS incorporates conformal risk control to ensure marginal coverage. Experiments on CIFAR-10 and CIFAR-100 datasets, utilizing deep ensembles, MC dropout, and evidential models, demonstrate that BPS consistently achieves better conditional coverage compared to APS, particularly in regions of low epistemic uncertainty, with comparable set sizes.

Key takeaway

For Machine Learning Engineers deploying models in safety-critical applications, you should consider implementing Bernoulli Prediction Sets (BPS) to robustly quantify and communicate predictive uncertainty. BPS provides optimal, smallest prediction sets with conditional coverage, especially when dealing with second-order predictors like deep ensembles or evidential models. This approach offers more reliable uncertainty estimates than traditional methods, improving trust and decision-making in high-stakes environments.

Key insights

Bernoulli Prediction Sets (BPS) optimally quantify uncertainty from second-order predictors, ensuring minimal prediction sets with conditional coverage.

Principles

• Epistemic Adaptivity: Smaller credal sets should yield smaller prediction sets.
• Optimality: Prediction sets should achieve conditional coverage with minimal size.
• Validity: Oracle first-order distribution must lie within the credal set.

Method

BPS solves a linear program to determine label inclusion probabilities, minimizing expected set size while satisfying conditional coverage for all distributions within a credal set. It uses conformal risk control for marginal guarantees with invalid credal sets.

In practice

• Integrate BPS with deep ensembles or MC dropout for robust uncertainty.
• Use BPS-nom for better conditional coverage in real-world scenarios.
• Apply conformal risk control to BPS for marginal coverage with invalid credal sets.

Topics

• Conformal Prediction
• Epistemic Uncertainty
• Credal Sets
• Bernoulli Prediction Sets
• Uncertainty Quantification
• Deep Ensembles

Code references

• alireza-javanmardi/conformal-BPS

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

Related on AIssential

• CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression — CREDO combines credal sets and conformal prediction to deliver calibrated, interpretable prediction intervals that explicitly quantify epistemic uncertainty.
• Hinge versus margin — the two nonconformity measures practitioners should understand — Conformal prediction yields prediction sets with finite-sample coverage guarantees, not probabilities.
• Possibilistic Predictive Uncertainty for Deep Learning — DAPPr uses possibility theory for principled, computationally efficient epistemic uncertainty quantification in deep learning.
• Safe Bayesian Optimization with Counterfactual Policies — Safe Bayesian optimization can use conformal prediction to manage uncertainty in unobserved counterfactual baselines, ensuring controlled constraint violations.
• The ninety-percent confidence that means nothing — and what does — Softmax outputs are not true probabilities and misrepresent classifier confidence; conformal prediction offers reliable coverage guarantees.
• Learning Credal Ensembles via Distributionally Robust Optimization — CreDRO quantifies epistemic uncertainty by modeling disagreement from potential train-test distribution shifts via distributionally robust optimization.

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