Feature Screening Based On Duality For Lasso-like Problems

Feature screening is a technique for sparse optimization problems,which is an important step in feature selection process.It can identify irrelevant variables in optimization problems,reduce model complexity,and improve model interpretability.In this paper,taking Lasso-like problem as research objects,the upper bound function of dual problem is obtained by the dual strong concave property,and then the neighborhood containing the dual optimal solution is constructed.Applying this general result to Fused Lasso which is a special Lasso-like problem,a safe region containing the dual optimal solution is obtained.When the dual feasible point is taken as the dual optimal solution of the previous step,we construct a Dome region which contains the dual optimal solution and the smallest sphere neighborhood which contains the Dome region.We show the smallest sphere containing the Dome region is consistent with the safe region constructed using subdifferential monotonicity by Wang,Fan and Ye.We give the selection method of dual feasible points to the general safe region of Fused Lasso.In addition,we apply the general results of Lasso-like to explore OWL regularized regression,construct the sphere neighborhood containing dual optimal solution and propose the safe screening rule.