Approximate Post-Selective Inference for Regression with the Group LASSO
Snigdha Panigrahi, Peter W MacDonald, Daniel Kessler; 24(79):1−49, 2023.
Abstract
In the absence of adjustments for selection bias, inference for the selected parameters after using the Group LASSO (or its generalized variants) is unreliable. Existing approaches for penalized Gaussian regression provide adjustments for selection events expressed as linear inequalities in the data variables. However, these approaches do not hold for selection with the Group LASSO and limit subsequent post-selective inference. This leaves key inferential questions unanswered, such as inference for the effects of selected variables on the outcome. In this paper, we propose a consistent, post-selective, Bayesian method to address these gaps. We derive a likelihood adjustment factor and an approximation that eliminates bias from the selection of groups. Our method recovers the effects of parameters within the selected groups while incurring only a small cost for bias adjustment, as demonstrated through experiments on simulated data and data from the Human Connectome Project.
[abs]