Conformal prediction constructs a confidence region for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal level without additional assumptions on their distribution. However, it requires a refitting procedure for all replacement candidates of the target response. In regression settings, this corresponds to an infinite number of model fit. Apart from relatively simple estimators that can be written as pieces of linear function of the response, efficiently computing such sets is difficult and is still considered as an open problem. We exploit the fact that, \emph{often}, conformal prediction sets are intervals whose boundaries can be efficiently approximated by classical root-finding software. We investigate how this approach can overcome many limitations of formerly used strategies and achieves calculations that have been unattainable so far. We discuss its complexity as well as its drawbacks and evaluate its efficiency through numerical experiments.

翻译：非正式预测根据以前对响应和特征的分布和可交换的相同观测结果,为特性矢量的未观测反应构建了一个信任区域。在任何名义水平上都具有覆盖保障,而没有额外的分布假设。然而,它要求对所有目标响应的替代候选人进行重新配置程序。在回归情况下,这相当于一个无限数量的适合模型。除了可以作为响应的线性功能碎片写成的相对简单的估计值之外,高效计算这类数据集是困难的,并且仍被视为一个未解决的问题。我们利用以下事实,即符合的预测数据集是典型的根基调查软件能够有效接近其边界的间隔点。我们调查这一方法如何能够克服以前使用的战略的许多局限性,并实现迄今为止无法实现的计算。我们讨论其复杂性及其缺陷,并通过数字实验评估其效率。