Journal of Data Science

We propose a scalable Bayesian network learning algorithm based on sparse Cholesky decomposition. Our approach only requires observational data and user-specified confidence level as inputs and can estimate networks with thousands of variables. The computational complexity of the proposed method is $O({p^{3}})$ for a graph with p vertices. Extensive numerical experiments illustrate the usefulness of our method with promising results. In simulation, the initial step in our approach also improves an alternative Bayesian network structure estimation method that uses an undirected graph as an input.