Learning Mixtures of DAG Models

We describe computationally efficient meth­ ods for learning mixtures in which each com­ ponent 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 in­ troduce a feasible approach in which param­ eter 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 ap­ proximation for model posterior probability and (2) the Expectation-Maximization algo­ rithm. We evaluate our procedure for select­ ing among MDAGs on synthetic and real ex­ amples.