Multicarving for high-dimensional post-selection inference

Christoph Schultheiss, Claude Renaux, Peter Bühlmann

Abstract: We consider post-selection inference for high-dimensional (generalized) linear models. Data carving from Fithian, Sun and Taylor is a promising technique to perform this task. However, it suffers from the instability of the model selector and hence, may lead to poor replicability, especially in high-dimensional settings. We propose the multicarve method inspired by multisplitting to improve upon stability and replicability. Furthermore, we extend existing concepts to group inference and illustrate the applicability of the methodology also for generalized linear models.