Learning mixtures of DAG models

B. Thiesson, C. Meek, D.M. Chickering, and D. Heckerman

December 1997

We describe computationally efficient methods for Bayesian model selection. The methods select among mixtures in which each mixture component is a directed acyclic graphical model (mixtures of DAGs or MDAGs), and can be applied to incomplete data sets. The model-selection criterion that we consider is the posterior probability of the model (structure) given data. Our model-selection problem is difficult because (1) the number of possible model structures grows super-exponentially with the number of random variables and (2) missing data necessitates the use of computationally slow approximations of model posterior probability. 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 the combinations of (1) a modified 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.

Publication type | TechReport |

URL | http://www.mkp.com/ |

Number | MSR-TR-97-30 |

Pages | 24 |

Institution | Microsoft Research, Redmond, WA |

Publisher | Morgan Kaufmann Publishers All copyrights reserved by Morgan Kaufmann Publishers 1998. |

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