Conformal prediction constructs a confidence set 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. Its computation deplorably 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 algorithm. We investigate how this approach can overcome many limitations of formerly used strategies and we discuss its complexity and drawbacks.
翻译:非正式预测根据先前相同分布和互换的对响应和特征的观测结果,为特性矢量的未观测反应建立了一套信任,在任何名义水平上保证覆盖,而不对其分布附加假设,其计算极其需要为所有目标响应的替代候选人重新设置一个程序。在回归情况下,这相当于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,而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定期的,其边界可以有效地被传统的根基调查算法所近似。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,我们讨论其复杂性和缺陷。