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.

翻译：全保形预测是一种框架，能够为广泛类型的估计器隐式构建无分布置信预测区域。然而，该框架的一个经典局限在于置信预测区域的计算通常不可行，因为这需要训练无限多个估计器（例如在实值预测任务中）。本研究的主要目标是提出一种通用策略，用于设计可高效计算的、对全保形预测区域的紧致近似。伴随这一近似置信区域，我们基于损失函数与评分函数的平滑性假设，建立了对该近似紧致性的理论量化。本文引入了"厚度"这一新概念，用以量化近似置信区域与全保形置信区域之间的差异。