Controlling false positive selections in high-dimensional regression and causal inference

Abstract

Guarding against false positive selections is important in many applications. We discuss methods based on subsampling and sample splitting for controlling the expected number of false positives and assigning p-values. They are generic and especially useful for high-dimensional settings. We review encouraging results for regression, and we discuss new adaptations and remaining challenges for selecting relevant variables, based on observational data, having a causal or interventional effect on a response of interest.