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.

我们从一致稳定性的角度研究全面稳定、杰克刀加和CV+预测区域的训练条件覆盖界限，这在具有凸正则化的再现核希尔伯特空间上的经验风险最小化中可靠，我们通过对（估计的）预测函数的集中性论证得出有限维模型的覆盖界限，并将其与岭回归下的现有界限进行比较。

训练条件覆盖界限对于均匀稳定学习算法的影响