MAGIC: a general, powerful and tractable method for selective inference
  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. 
Xiaoying Tian, Nan Bi and Jonathan Taylor
math.ST stat.TH