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Causal discovery, the learning of causality in a data mining scenario, hasbeen of strong scientific and theoretical interest as a starting point toidentify "what causes what?" Contingent on assumptions and a proper learningalgorithm, it is sometimes possible to identify and accurately estimate acausal directed acyclic graph (DAG), as opposed to a Markov equivalence classof graphs that gives ambiguity of causal directions. The focus of this paper isin highlighting the identifiability and estimation of DAGs with general errordistributions through a general sequential sorting procedure that ordersvariables one at a time, starting at root nodes, followed by children of theroot nodes, and so on until completion. We demonstrate a novel application ofthis general approach to estimate the topological ordering of a DAG. At eachstep of the procedure, only simple likelihood ratio scores are calculated onregression residuals to decide the next node to append to the current partialordering. The computational complexity of our algorithm on a p-node problem isO(pd), where d is the maximum neighborhood size. Under mild assumptions, thepopulation version of our procedure provably identifies a true ordering of theunderlying DAG. We provide extensive numerical evidence to demonstrate thatthis sequential procedure scales to possibly thousands of nodes and works wellfor high-dimensional data. We accompany these numerical experiments with anapplication to a single-cell gene expression dataset.

Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores