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

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.

References in corpus (4)

• Valid post-selection inference
• Optimal Inference After Model Selection
• Selective inference with a randomized response
• Selective inference with unknown variance via the square-root LASSO

Cited by in corpus (6)

• Why Adaptively Collected Data Have Negative Bias and How to Correct for It
• Selective inference with a randomized response
• Bootstrap inference after using multiple queries for model selection
• An MCMC-free approach to post-selective inference
• Information, Privacy and Stability in Adaptive Data Analysis
• Inference After Selecting Plausibly Valid Instruments with Application to Mendelian Randomization