DPC (DPP) Screening Methods for Group Lasso
Publications
Notice that, the Enhanced DPP (EDPP) rule to appear in JMLR is an improved version of the EDPP rule in the NIPS paper. They are NOT the same. The EDPP rule in the NIPS paper refers to “Improvement 1” in the journal version. The EDPP rule introduced below refers to the one in the journal version. Formulation of Group LassoLet denote the dimensional response vector and be the feature matrix. Let be the regularization parameter. With the group information available, the Group Lasso problem is formulated as the following optimization problem: The dual problem of Lasso is We denote the primal and dual optimal solutions of Lasso by and , respectively, which depend on the value of . and are related by Moreover, it is easy to see that the dual optimal solution is the projection of onto the dual feasible set, which is the intersection of a set of ellipsoids. DPC (EDPP) rule for Group LassoLet us define It is wellknown that , we have In other words, the Group Lasso problem admits closed form solutions when . Let and . We define DPC (EDPP) Screening Rule for Group Lasso
A Few More Comments of DPC (EDPP)
