The lasso [Tibshirani, 1996] refers to L1-regularization of linear models:
In group lasso [Yuan and Lin 2006], the D predictors are divided into G groups, and the g-th group has predictors. The regularization term becomes:
where denotes the L2-norm: . So, when all ‘s are 1, group lasso becomes lasso.
A further extension to group lasso is sparse group lasso:
But in practice, we may not need this very complex regularization.