提出高效近似全置信预测方法，解决计算不可行问题
Approximate full conformal prediction in an RKHS
- 基于再生核希尔伯特空间设计近似算法，避免无限次训练
- 理论证明近似精度与损失函数光滑性相关，可量化误差
- 适合需要高置信度且计算资源有限的机器学习应用
全置信预测是一种适用于多种估计器的分布无关置信预测区域构建框架。然而，其经典局限在于计算成本过高——例如实值预测需训练无穷多个估计器，通常不可行。本文提出一种通用策略，设计出可高效计算的紧致近似置信区域。同时建立理论框架，量化该近似的紧致性，依赖于损失函数和评分函数的光滑性假设。引入‘厚度’这一新概念，用于衡量近似区域与完整置信区域之间的差异。
原文摘要 · Abstract (English)
Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators. However, a classical limitation of the full conformal framework is the computation of the confidence prediction regions, which is usually impossible since it requires training infinitely many estimators (for real-valued prediction for instance). The main purpose of the present work is to describe a generic strategy for designing a tight approximation to the full conformal prediction region that can be efficiently computed. Along with this approximate confidence region, a theoretical quantification of the tightness of this approximation is developed, depending on the smoothness assumptions on the loss and score functions. The new notion of thickness is introduced for quantifying the discrepancy between the approximate confidence region and the full conformal one.
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