Estimation of Gaussian directed acyclic graphs using partial ordering information with an application to 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 data, 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.