Conformal prediction is a generic methodology for finite-sample valid distribution-free prediction. This technique has garnered a lot of attention in the literature partly because it can be applied with any machine learning algorithm that provides point predictions to yield valid prediction regions. Of course, the efficiency (width/volume) of the resulting prediction region depends on the performance of the machine learning algorithm. In the context of point prediction, several techniques (such as cross-validation) exist to select one of many machine learning algorithms for better performance. In contrast, such selection techniques are seldom discussed in the context of set prediction (or prediction regions). In this paper, we consider the problem of obtaining the smallest conformal prediction region given a family of machine learning algorithms. We provide two general-purpose selection algorithms and consider coverage as well as width properties of the final prediction region. The first selection method yields the smallest width prediction region among the family of conformal prediction regions for all sample sizes but only has an approximate coverage guarantee. The second selection method has a finite sample coverage guarantee but only attains close to the smallest width. The approximate optimal width property of the second method is quantified via an oracle inequality. As an illustration, we consider the use of aggregation of non-parametric regression estimators in the split conformal method with the absolute residual conformal score.
Efficient conformal prediction intervals for time series: Online PID-Expert aggregation
School of Economics and Management, Beihang University（北京航空航天大学经济管理学院）；Beijing Shuji Intelligent Technology Co., Ltd.（北京数智科技有限公司）；Center for Forecasting Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院预测科学中心）
Conformal prediction after data-dependent model selection
University of Chicago（芝加哥大学）；Department of Statistics, University of California, Irvine（加州大学尔湾分校统计系）；Department of Statistics, University of Chicago（芝加哥大学统计系）
CoCopula: Conformal Calibration and Copula Aggregation for Reliable Renewable Energy Forecasting
NSF Artificial Intelligence Institute for Advances in Optimization（NSF人工智能优化研究所）；H. Milton Stewart School of Industrial and Systems Engineering（H. Milton Stewart工业与系统工程学院）；Georgia Institute of Technology（佐治亚理工学院）
Mathematics Department, The Hong Kong University of Science（香港科学与技术大学数学系）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计与数据科学系）；Data Science, University of Pennsylvania, Philadelphia, PA, USA（宾夕法尼亚大学数据科学）
Eletrcicité De France R&D（法国电力公司研发部）；INRIA Sophia-Antipolis（法国国家信息与自动化研究所索菲亚-昂蒂波利斯分所）；CMAP, Ecole Polytechnique, IP Paris（巴黎综合理工学院应用数学与概率中心（CMAP））；FiME；IDESP；Eletrcicité De France R&D, Palaiseau, France（法国电力公司研发部（帕莱索））；INRIA Sophia-Antipolis, Montpellier, France（法国国家信息与自动化研究所索菲亚-昂蒂波利斯分所（蒙彼利埃））；CMAP, Ecole Polytechnique, IP Paris, Palaiseau, France（巴黎综合理工学院应用数学与概率中心（CMAP，帕莱索））；FiME, Palaiseau, France（FiME（帕莱索））；IDESP, Montpellier, France（IDESP（蒙彼利埃））
Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference
Department of Statistics, Stanford University（斯坦福大学统计学系）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计学与数据科学系）；Department of Mathematics, Stanford University（斯坦福大学数学系）
Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data
University of Connecticut（康涅狄格大学）；University of Connecticut Health Center (UCHC)（康涅狄格大学健康中心）；Weill Cornell Medical College, Cornell University（康奈尔大学威尔医学院）
