CausNet-partial: ‘Partial Generational Orderings’ based search for optimal sparse Bayesian networks via dynamic programming with parent set constraints

In our recent work, we developed a novel dynamic programming algorithm to find optimal Bayesian networks with parent set constraints. This ‘generational orderings’ based dynamic programming algorithm—CausNet—efficiently searches the space of possible Bayesian networks. The method is designed for continuous as well as discrete data, and continuous, discrete and survival outcomes. In the present work, we develop a variant of CausNet—CausNet-partial—where we introduce the space of ‘partial generational orderings’, which is a novel way to search for small and sparse optimal Bayesian networks from large dimensional data. We test this method both on simulated and real data. In simulations, CausNet-partial shows superior performance when compared with three state-of-the-art algorithms. We apply it also to a benchmark discrete Bayesian network ALARM, a Bayesian network designed to provide an alarm message system for patient monitoring. We first apply the original CausNet and then CausNet-partial, varying the partial order from 5 to 2. CausNet-partial discovers small sparse networks with drastically reduced runtime as expected from theory. To further demonstrate the efficacy of CausNet-partial, we apply it to an Ovarian Cancer gene expression dataset with 513 genes and a survival outcome. Our algorithm is able to find optimal Bayesian networks with different number of nodes as we vary the partial order. On a personal computer with a 2.3 GHz Intel Core i9 processor with 16 GB RAM, each processing takes less than five minutes. Our ‘partial generational orderings’ based method CausNet-partial is an efficient and scalable method for finding optimal sparse and small Bayesian networks from high dimensional data.