Conformal prediction is a popular tool for providing valid prediction sets
for classification and regression problems, without relying on any
distributional assumptions on the data. While the traditional description of
conformal prediction starts with a nonconformity score, we provide an alternate
(but equivalent) view that starts with a sequence of nested sets and calibrates
them to find a valid prediction set. The nested framework subsumes all
nonconformity scores, including recent proposals based on quantile regression
and density estimation. While these ideas were originally derived based on
sample splitting, our framework seamlessly extends them to other aggregation
schemes like cross-conformal, jackknife+ and out-of-bag methods. We use the
framework to derive a new algorithm (QOOB, pronounced cube) that combines four
ideas: quantile regression, cross-conformalization, ensemble methods and
out-of-bag predictions. We develop a computationally efficient implementation
of cross-conformal, that is also used by QOOB. In a detailed numerical
investigation, QOOB performs either the best or close to the best on all
simulated and real datasets. Code for QOOB is available at
this https URL

本文讲述了一个基于嵌套的框架的可靠预测方法，使用该方法，我们设计并实现了 QOOB 算法，它将四个想法整合在一起：分位数回归、交叉合规化、集成方法和袋外预测。在模拟和真实数据集上的实验中，QOOB 的表现要么最佳，要么接近最佳。