The training-conditional coverage performance of the conformal prediction is known to be empirically sound. Recently, there have been efforts to support this observation with theoretical guarantees. The training-conditional coverage bounds for jackknife+ and full-conformal prediction regions have been established via the notion of $(m,n)$-stability by Liang and Barber~[2023]. Although this notion is weaker than uniform stability, it is not clear how to evaluate it for practical models. In this paper, we study the training-conditional coverage bounds of full-conformal, jackknife+, and CV+ prediction regions from a uniform stability perspective which is known to hold for empirical risk minimization over reproducing kernel Hilbert spaces with convex regularization. We derive coverage bounds for finite-dimensional models by a concentration argument for the (estimated) predictor function, and compare the bounds with existing ones under ridge regression.

翻译：共形预测的训练条件覆盖性能在经验上表现良好。近期，学界致力于为此观测现象提供理论保证。Liang和Barber[2023]通过$(m,n)$-稳定性概念，建立了刀切法与全共形预测区域的训练条件覆盖界。尽管该概念比均匀稳定性更弱，但其在实际模型中的评估方法尚不明确。本文从均匀稳定性视角研究全共形、刀切法和CV+预测区域的训练条件覆盖界——该稳定性已知在具有凸正则化的再生核希尔伯特空间上，对经验风险最小化成立。我们通过（估计的）预测函数的集中性论证，推导出有限维模型的覆盖界，并在岭回归条件下与现有界进行比较。