Conditional validity and length efficiency are two crucial aspects of conformal prediction (CP). Achieving conditional validity ensures accurate uncertainty quantification for data subpopulations, while proper length efficiency ensures that the prediction sets remain informative and non-trivial. Despite significant efforts to address each of these issues individually, a principled framework that reconciles these two objectives has been missing in the CP literature. In this paper, we develop Conformal Prediction with Length-Optimization (CPL) - a novel framework that constructs prediction sets with (near-) optimal length while ensuring conditional validity under various classes of covariate shifts, including the key cases of marginal and group-conditional coverage. In the infinite sample regime, we provide strong duality results which indicate that CPL achieves conditional validity and length optimality. In the finite sample regime, we show that CPL constructs conditionally valid prediction sets. Our extensive empirical evaluations demonstrate the superior prediction set size performance of CPL compared to state-of-the-art methods across diverse real-world and synthetic datasets in classification, regression, and text-related settings.

研究发展了一种新颖的基于长度优化的一致性预测框架（CPL），能够在不同类别的协变量转移下确保条件有效性，并构建出（接近）最优长度的预测集合，通过广泛的实证评估验证了其在分类、回归和文本相关设置方面相较于最新方法在预测集大小性能方面的优越性。

置信度预测中的长度优化