Learning Mixtures of DAG Models
This addresses the challenge of efficiently learning complex probabilistic models for researchers in machine learning and statistics, though it appears incremental as it combines existing approximations and algorithms.
The paper tackles the problem of learning mixtures of directed acyclic graphical models (MDAGs) by introducing a computationally efficient method that interleaves parameter and structure search, treating expected data as real data. The result is evaluated on synthetic and real examples, showing feasibility where simple search-and-score algorithms fail.
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.