We consider the problems of estimation and selection of parameters endowed
with a known group structure, when the groups are assumed to be sign-coherent,
that is, gathering either non-negative, non-positive or null parameters. To
tackle this problem we propose a new penalty that we call the cooperative-Lasso
penalty. We derive the optimality conditions defining the cooperative-Lasso
estimate for generalized linear models and propose an efficient active set
algorithm suited to high-dimensional problems.
We present a weighted-Lasso method to infer the parameters of a first-order
vector auto-regressive model that describes time course expression data
generated by directed gene-to-gene regulation networks. These networks are
assumed to own a priori internal structures of connectivity which drive the
inference method. Solution to the optimization problem is efficiently computed
using an active-set algorithm. We illustrate the performance both on synthetic
data and on the yeast regulation network by analyzing Spellman et al's dataset.