Inferring large graphs with an l1-penalized likelihood formulation and a hybrid genetic algorithm

Magali Champion (1) , Victor Picheny (2) , Matthieu Vignes (3)

1 Stanford School of Medicine [Stanford]
2 INRA - Institut National de la Recherche Agronomique
3 Massey University

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 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.

Mots clés: Directed Acyclic Graphs; Lasso; Convex program; Optimization

Domaines: Statistiques [math.ST]

Magali Champion, Victor Picheny, Matthieu Vignes. Inferring large graphs with an l1-penalized likelihood formulation and a hybrid genetic algorithm. 2015. ⟨hal-01172745v1⟩