  We address the issue of recovering the structure of large sparse directed
acyclic graphs from noisy observations of the system. We propose a novel
procedure based on a specific formulation of the l1-norm regularized maximum
likelihood, which decomposes the graph estimation into two optimization
sub-problems: topological structure and node order learning. We provide oracle
inequalities for the graph estimator, as well as an algorithm to solve the
induced optimization problem, in the form of a convex program embedded in a
genetic algorithm. We apply our method to various data sets (including data
from the DREAM4 challenge) and show that it compares favorably to
state-of-the-art methods.
