Inferring large graphs using l1-penalized likelihood

TL;DR

This paper introduces a new l1-penalized likelihood approach for inferring large sparse directed acyclic graphs, effectively decomposing the problem into structure and order learning, with demonstrated superior performance on real data.

Contribution

It presents a novel convex optimization-based method for large graph inference that combines topological and node order learning, validated on real datasets.

Findings

Method outperforms existing techniques on benchmark datasets.

Provides theoretical guarantees via oracle inequalities.

Efficient algorithm combining convex programming and genetic algorithms.

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.