  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.
