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This paper considers inference of causal structure in a class of graphicalmodels called "conditional DAGs". These are directed acyclic graph (DAG) modelswith two kinds of variables, primary and secondary. The secondary variables areused to aid in estimation of causal relationships between the primaryvariables. We give causal semantics for this model class and prove that, undercertain assumptions, the direction of causal influence is identifiable from thejoint observational distribution of the primary and secondary variables. Ascore-based approach is developed for estimation of causal structure usingthese models and consistency results are established. Empirical resultsdemonstrate gains compared with formulations that treat all variables on anequal footing, or that ignore secondary variables. The methodology is motivatedby applications in molecular biology and is illustrated here using simulateddata and in an analysis of proteomic data from the Cancer Genome Atlas.

Estimating causal structure using conditional DAG models