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arXiv · 1607.02630

MAGIC: a general, powerful and tractable method for selective inference

Xiaoying Tian·Nan Bi·Jonathan Taylor
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Abstract

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 $\ell_1$ 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 $\ell_1$ penalized optimization problem including the Lasso, logistic Lasso and neighborhood selection in graphical models, all of which we consider in this paper.

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Xiaoying Tian, Nan Bi, Jonathan Taylor. 2016-07-09. MAGIC: a general, powerful and tractable method for selective inference. https://arxiv.org/abs/1607.02630

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