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Estimating a directed acyclic graph (DAG) from observational data representsa canonical learning problem and has generated a lot of interest in recentyears. Research has focused mostly on the following two cases: when noinformation regarding the ordering of the nodes in the DAG is available, andwhen a domain-specific complete ordering of the nodes is available. In thispaper, motivated by a recent application in dairy science, we develop a methodfor DAG estimation for the middle scenario, where partition based partialordering of the nodes is known based on domain specific knowledge.We develop anefficient algorithm that solves the posited problem, coined Partition-DAG.Through extensive simulations using the DREAM3 Yeast data, we illustrate thatPartition-DAG effectively incorporates the partial ordering information toimprove both speed and accuracy. We then illustrate the usefulness ofPartition-DAG by applying it to recently collected dairy cattle data, andinferring relationships between various variables involved in dairyagroecosystems.

Estimation of Gaussian directed acyclic graphs using partial ordering information with an application to dairy cattle data