In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research has considered relaxations of full conditional guarantees, relying on some predefined uncertainty structures. Departing from this line of thinking, we propose Partition Learning Conformal Prediction (PLCP), a framework to improve conditional validity of prediction sets through learning uncertainty-guided features from the calibration data. We implement PLCP efficiently with alternating gradient descent, utilizing off-the-shelf machine learning models. We further analyze PLCP theoretically and provide conditional guarantees for infinite and finite sample sizes. Finally, our experimental results over four real-world and synthetic datasets show the superior performance of PLCP compared to state-of-the-art methods in terms of coverage and length in both classification and regression scenarios.

翻译：本文聚焦于具有条件保证的分保形预测问题。先前研究表明，构建具有完全条件覆盖保证的非平凡预测集是不可能的。大量研究考虑了完全条件保证的松弛形式，并依赖于某些预定义的不确定性结构。区别于这一思路，我们提出分区学习分保形预测（PLCP）框架，通过从校准数据中学习不确定性引导的特征，来提高预测集的条件有效性。我们利用交替梯度下降法高效实现PLCP，并采用现成的机器学习模型。我们进一步对PLCP进行理论分析，给出了无限样本和有限样本量下的条件保证。最后，我们在四个真实世界和合成数据集上的实验结果表明，在分类和回归场景中，PLCP在覆盖率和长度方面均优于现有最先进方法。