Selective Inference for Group-Sparse Linear Models

TL;DR

This paper develops statistical inference tools for group-sparse models, allowing for valid confidence intervals and p-values after variable group selection using methods like group lasso and forward stepwise regression.

Contribution

It provides the first precise distributional results for projections in group-sparse models, enabling valid post-selection inference for various group selection methods.

Findings

Validated inference procedures on simulated data

Applied methods to health record data

Demonstrated accurate confidence intervals and p-values

Abstract

We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of the magnitude of the projection of the data onto a given subspace, and enables us to develop inference procedures for a broad class of group-sparse selection methods, including the group lasso, iterative hard thresholding, and forward stepwise regression. We give numerical results to illustrate these tools on simulated data and on health record data.