Conformal prediction provides distribution-free prediction sets with finite-sample conditional guarantees. We build upon the RKHS-based framework of Gibbs et al. (2023), which leverages families of covariate shifts to provide approximate conditional conformal prediction intervals, an approach with strong theoretical promise, but with prohibitive computational cost. To bridge this gap, we develop a stable and efficient algorithm that computes the full solution path of the regularized RKHS conformal optimization problem, at essentially the same cost as a single kernel quantile fit. Our path-tracing framework simultaneously tunes hyperparameters, providing smoothness control and data-adaptive calibration. To extend the method to high-dimensional settings, we further integrate our approach with low-rank latent embeddings that capture conditional validity in a data-driven latent space. Empirically, our method provides reliable conditional coverage across a variety of modern black-box predictors, improving the interval length of Gibbs et al. (2023) by 30%, while achieving a 40-fold speedup.

翻译：共形预测提供了具有有限样本条件保证的无分布预测集。我们基于Gibbs等人（2023）的RKHS框架，该框架利用协变量偏移族提供近似条件共形预测区间，这一方法具有强大的理论前景，但计算成本过高。为弥补这一差距，我们开发了一种稳定高效的算法，该算法以与单次核分位数拟合基本相同的计算成本，计算正则化RKHS共形优化问题的完整解路径。我们的路径追踪框架同时调整超参数，提供平滑控制和数据自适应校准。为将该方法扩展到高维场景，我们进一步将我们的方法与低秩潜在嵌入相结合，该嵌入在数据驱动的潜在空间中捕捉条件有效性。实验表明，我们的方法在各种现代黑箱预测器上提供了可靠的条件覆盖，将Gibbs等人（2023）的区间长度改善30%，同时实现了40倍的加速。