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Learning the directed acyclic graph (DAG) structure of a Bayesian networkfrom observational data is a notoriously difficult problem for which manyhardness results are known. In this paper we propose a provably polynomial-timealgorithm for learning sparse Gaussian Bayesian networks with equal noisevariance --- a class of Bayesian networks for which the DAG structure can beuniquely identified from observational data --- under high-dimensionalsettings. We show that $O(k^4 \log p)$ number of samples suffices for ourmethod to recover the true DAG structure with high probability, where $p$ isthe number of variables and $k$ is the maximum Markov blanket size. We obtainour theoretical guarantees under a condition called Restricted Strong AdjacencyFaithfulness, which is strictly weaker than strong faithfulness --- a conditionthat other methods based on conditional independence testing need for theirsuccess. The sample complexity of our method matches the information-theoreticlimits in terms of the dependence on $p$. We show that our method out-performsexisting state-of-the-art methods for learning Gaussian Bayesian networks interms of recovering the true DAG structure while being comparable in speed toheuristic methods.

Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity