Selective inference is a recent research topic that tries to perform valid inference after using the data to select a reasonable statistical model. We propose MAGIC, a new method for selective inference that is general, powerful and tractable. MAGIC is a method for selective inference after solving a convex optimization problem with smooth loss and ℓ1 penalty. Randomization is incorporated into the optimization problem to boost statistical power. Through reparametrization, MAGIC reduces the problem into a sampling problem with simple constraints. MAGIC applies to many ℓ1 penalized optimization problem including the Lasso, logistic Lasso and neighborhood selection in graphical models, all of which we consider in this paper.
@article{arxiv.1607.02630,
title = {MAGIC: a general, powerful and tractable method for selective inference},
author = {Xiaoying Tian and Nan Bi and Jonathan Taylor},
journal= {arXiv preprint arXiv:1607.02630},
year = {2016}
}