Conformal Inference (CI) is a popular approach for generating finite sample prediction intervals based on the output of any point prediction method when data are exchangeable. Adaptive Conformal Inference (ACI) algorithms extend CI to the case of sequentially observed data, such as time series, and exhibit strong theoretical guarantees without having to assume exchangeability of the observed data. The common thread that unites algorithms in the ACI family is that they adaptively adjust the width of the generated prediction intervals in response to the observed data. We provide a detailed description of five ACI algorithms and their theoretical guarantees, and test their performance in simulation studies. We then present a case study of producing prediction intervals for influenza incidence in the United States based on black-box point forecasts. Implementations of all the algorithms are released as an open-source R package, AdaptiveConformal, which also includes tools for visualizing and summarizing conformal prediction intervals.

翻译：共形推断是一种在数据可交换条件下，基于任意点预测方法输出生成有限样本预测区间的流行方法。自适应共形推断算法将共形推断扩展至顺序观测数据（如时间序列）场景，在无需假设观测数据可交换性的前提下展现出强理论保证。ACI系列算法的共同特点是能够根据观测数据自适应调整生成预测区间的宽度。我们详细描述了五种ACI算法及其理论保证，并通过模拟研究评估其性能。随后通过基于黑箱点预测对美国流感发病率生成预测区间的案例研究进行验证。所有算法均已实现为开源R语言包AdaptiveConformal，其中还包含用于可视化和汇总共形预测区间的工具。