  Directed acyclic graphs (DAGs) are commonly used to model causal
relationships among random variables. In general, learning the DAG structure is
both computationally and statistically challenging. Moreover, without
additional information, the direction of edges may not be estimable from
observational data. In contrast, given a complete causal ordering of the
variables, the problem can be solved efficiently, even in high dimensions. In
this paper, we consider the intermediate problem of learning DAGs when a
partial causal ordering of variables is available. We propose a general
estimation framework for leveraging the partial ordering and present efficient
estimation algorithms for low- and high-dimensional problems. The advantages of
the proposed framework are illustrated via numerical studies.
