Estimation of Gaussian directed acyclic graphs using partial ordering information with applications to DREAM3 networks and dairy cattle data

Estimating a directed acyclic graph (DAG) from observational data represents a canonical learning problem and has generated a lot of interest in recent years. Research has focused mostly on the following two cases: when no information regarding the ordering of the nodes in the DAG is available, and when a domain-specific complete ordering of the nodes is available. In this paper, motivated by a recent application in dairy science, we develop a method for DAG estimation for the middle scenario, where partition based partial ordering of the nodes is known based on domain-specific knowledge. We develop an efficient algorithm that solves the posited problem, coined Partition-DAG. Through extensive simulations using the DREAM3 Yeast networks, we illustrate that Partition-DAG effectively incorporates the partial ordering information to improve both speed and accuracy. We then illustrate the usefulness of Partition-DAG by applying it to recently collected dairy cattle data, and inferring relationships between various variables involved in dairy agroecosystems. two sets (ParDAG-2), PC algorithm (PC), Stable PC algorithm (PC-STAB), Parallel-PC algorithm (PC-PAR), PC algorithm with background knowledge partition (PCBGK-2). algorithm variants partially oriented values non-oriented