The Degrees of Freedom of the Group Lasso
  This paper studies the sensitivity to the observations of the block/group Lasso solution to an overdetermined linear regression model. Such a regularization is known to promote sparsity patterns structured as nonoverlapping groups of coefficients. Our main contribution provides a local parameterization of the solution with respect to the observations. As a byproduct, we give an unbiased estimate of the degrees of freedom of the group Lasso. Among other applications of such results, one can choose in a principled and objective way the regularization parameter of the Lasso through model selection criteria. 
Samuel Vaiter (CEREMADE), Charles Deledalle (CEREMADE), Gabriel   Peyr\'e (CEREMADE), Jalal Fadili (GREYC), Charles Dossal (IMB)
math.ST stat.TH