  We describe computationally efficient methods for learning mixtures in which
each component is a directed acyclic graphical model (mixtures of DAGs or
MDAGs). We argue that simple search-and-score algorithms are infeasible for a
variety of problems, and introduce a feasible approach in which parameter and
structure search is interleaved and expected data is treated as real data. Our
approach can be viewed as a combination of (1) the Cheeseman--Stutz asymptotic
approximation for model posterior probability and (2) the
Expectation--Maximization algorithm. We evaluate our procedure for selecting
among MDAGs on synthetic and real examples.
