Sorted L-One Penalized Estimator

Sorted L-One Penalized Estimator is a relatively new convex optimization procedure for identifying predictors in large data bases. In this lecture we will present the method, some theoretical and empirical results illustrating its properties and the applications in the context of genomic and medical data. Apart from the classical version of SLOPE we will also discuss its spike and slab version, aimed at reducing the bias of estimators of regression coefficients. When discussing SLOPE we will also present some new theoretical results on the probability of discovering the true model by LASSO (which is a specific instance of SLOPE) and its thresholded version