Post-selection inference with kernels

The most common model selection approaches rely on univariate linear
measures of association between each feature and the outcome. The
post-selection inference framework then makes it possible to perform
valid statistical inference (such as evaluating the association of a
joint model built from selected variables with the outcome) by
conditioning on the selection event. By contrast, kernel-based
procedures allow to account for nonlinear effects and interactions
between features. We show how to extend the post-selection inference
framework to stepwise kernel selection procedures, which we model as a
succession of constraints that are quadratic in the outcome variable.
Our work is motivated by its application to intragenic epistasis
detection in high-dimensional genomics data.

Slim et al. (2019) kernelPSI: a post-selection inference framework for
nonlinear variable selection, Proceedings of ICML 97:5857—5865.