Beyond Conformal Predictors: Adaptive Conformal Inference with Confidence Predictors

Conformal prediction (CP) is a robust framework for distribution-free uncertainty quantification, but it requires exchangeable data to ensure valid prediction sets at a user-specified significance level. When this assumption is violated, as in time-series or other structured data, the validity guarantees of CP no longer hold. Adaptive conformal inference (ACI) was introduced to address this limitation by adjusting the significance level dynamically, ensuring finite-sample coverage guarantees even for non-exchangeable data. In this paper, we show that ACI does not require the use of conformal predictors; instead, it can be implemented with the more general confidence predictors, which are computationally simpler and still maintain the crucial property of nested prediction sets. Through experiments on synthetic and real-world data, we demonstrate that confidence predictors can perform comparably to, or even better than, conformal predictors, particularly in terms of computational efficiency. These findings suggest that confidence predictors represent a viable and efficient alternative to conformal predictors in non-exchangeable data settings, although further studies are needed to identify when one method is superior.