Inferring large graphs using l1-penalized likelihood

Abstract

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.

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Cited by in corpus (6)

• Learning Large-Scale Bayesian Networks with the sparsebn Package
• Optimizing regularized Cholesky score for order-based learning of Bayesian networks
• Inferring large graphs using l1-penalized likelihood
• Mode jumping MCMC for Bayesian variable selection in GLMM
• Mapping Energy Landscapes of Non-Convex Learning Problems
• Estimation of Gaussian directed acyclic graphs using partial ordering information with an application to dairy cattle data