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，能够为广泛类别的估计量隐式构建分布无关的置信预测区域。然而，全保形框架的一个经典局限在于置信预测区域的计算，这通常无法实现，因为它需要训练无限多个估计量（例如在实值预测中）。本文的主要目的是描述一种通用策略，用于设计可高效计算的、对全保形预测区域的紧致近似。除了这一近似置信区域外，我们还基于损失函数和评分函数的平滑性假设，发展了关于该近似紧致性的理论量化方法。本文引入了厚度的新概念，用于量化近似置信区域与全保形区域之间的差异。