text: This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
  @cite_13: Let A be an M by N matrix (M 1 - 1 d, and d = Omega(log(1 isin) isin3) . The relaxation given in (*) can be solved in polynomial time using semi-definite programming.
summary: In @cite_13 , the authors attempted to derive a bound on the number of samples needed to recover block sparse signals, where the coefficients in each block are either all zero or all nonzero. In our terminology, this corresponds to the case of group sparsity with equal size groups. The algorithm considered there is a special case of ) with @math . However, their result is very loose, and does not demonstrate the advantage of group Lasso over standard Lasso.