The group Lasso

Abstract

In many applications, the high-dimensional parameter vector carries a structure. Among the simplest is a group structure where the parameter is partitioned into disjoint pieces. This occurs when dealing with factor variables or in connection with basis expansions in high-dimensional additive models as discussed in Chapters 5 and 8. The goal is high-dimensional estimation in linear or generalized linear models being sparse with respect to whole groups. The group Lasso, proposed by Yuan and Lin (2006) achieves such group sparsity. We discuss in this chapter methodological aspects, and we develop the details for efficient computational algorithms which are more subtle than for non-group problems.