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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  1-norm regularized maximumlikelihood, which decomposes the graph estimation into two optimization sub-problems: topological structure and node order learning. We provide convergence 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. This algorithm is available onCRANas theRpackage GADAG

Inferring large graphs using $$\ell _1$$ ℓ 1 -penalized likelihood