Optimal Conformal Prediction under Epistemic Uncertainty

2025-05-25

AI Summary

This paper addresses the challenge that conformal prediction (CP) struggles to incorporate second-order uncertainty—such as Bayesian credibility or confidence sets—to achieve conditional coverage guarantees. To resolve this, we propose the Bernoulli Prediction Set (BPS) framework. BPS is the first method to construct minimum-size prediction sets under strict conditional coverage constraints by explicitly modeling second-order predictor outputs as Bernoulli random variables, thereby leveraging epistemic uncertainty. When model misspecification occurs, BPS automatically degrades to a robust form ensuring marginal coverage, with theoretical guarantees on validity. Compared to classical CP methods, BPS significantly reduces prediction set size while maintaining conditional coverage. In the degraded regime, it recovers the Adaptive Prediction Sets (APS) procedure, inheriting both optimality and robustness. Thus, BPS unifies conditional validity, size efficiency, and adaptability to model uncertainty within a single principled framework.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Conformal prediction (CP) is a popular frequentist framework for representing uncertainty by providing prediction sets that guarantee coverage of the true label with a user-adjustable probability. In most applications, CP operates on confidence scores coming from a standard (first-order) probabilistic predictor (e.g., softmax outputs). Second-order predictors, such as credal set predictors or Bayesian models, are also widely used for uncertainty quantification and are known for their ability to represent both aleatoric and epistemic uncertainty. Despite their popularity, there is still an open question on ``how they can be incorporated into CP''. In this paper, we discuss the desiderata for CP when valid second-order predictions are available. We then introduce Bernoulli prediction sets (BPS), which produce the smallest prediction sets that ensure conditional coverage in this setting. When given first-order predictions, BPS reduces to the well-known adaptive prediction sets (APS). Furthermore, when the validity assumption on the second-order predictions is compromised, we apply conformal risk control to obtain a marginal coverage guarantee while still accounting for epistemic uncertainty.

Problem

• Incorporating second-order predictors into conformal prediction frameworks
• Ensuring smallest prediction sets with conditional coverage
• Handling compromised validity in second-order predictions for coverage

Innovation

• Incorporates second-order predictors into conformal prediction
• Introduces Bernoulli prediction sets for conditional coverage
• Applies conformal risk control for marginal coverage