Optimal Conformal Prediction under Epistemic Uncertainty

TL;DR

This paper introduces Bernoulli prediction sets (BPS) for conformal prediction that optimally incorporate second-order uncertainty, providing smaller prediction sets with coverage guarantees even under epistemic uncertainty.

Contribution

It proposes BPS, a novel conformal prediction method that effectively integrates second-order uncertainty, and extends to conformal risk control for robustness against validity violations.

Findings

BPS produces smaller prediction sets with guaranteed coverage.

BPS reduces to adaptive prediction sets when using first-order predictions.

Conformal risk control maintains marginal coverage under validity compromises.

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.