CNB: A Bayesian Nonparametric Approach to Optimal Conformal Prediction

Junxi Zhang, Linglong Kong, Bei Jiang

Keywords: Conformal prediction, Bayesian nonparametric mixture models, Optimal conformal set

TL;DR: We propose Conformal Nonparametric Bayes (CNB), which integrates Bayesian nonparametric procedures into conformal prediction to yield optimal prediction sets without prior knowledge of the true model.

Abstract: Conformal Bayes has been shown to yield the optimal (i.e., smallest expected volume) prediction sets among all prediction sets with a $(1-\alpha)$ coverage guarantee if the model is correctly specified. However, a critical issue arises when the model is misspecified: the resulting prediction sets, while still satisfying the frequentist coverage guarantee, can become inefficient and suboptimal. To address this limitation, we propose a conformal nonparametric Bayes (CNB) prediction approach, an innovative solution that incorporates Bayesian nonparametric procedures within conformal prediction. This hybrid offers significant improvements over existing methods in three key aspects: (i) it retains the strengths of the full conformal Bayes, (ii) the Bayesian nonparametric layer enhances robustness under model uncertainty and induces endogenous clustering in the data, (iii) model complexity adapts to the data. Theoretically, we show that the resulting CNB prediction sets are valid and will converge to the optimal level of efficiency. The proposed CNB prediction approach provides significant improvements over existing methods while ensuring optimality and precise uncertainty quantification.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 2254