Learning Mixtures of DAG Models

TL;DR

This paper introduces an efficient method for learning mixtures of directed acyclic graphical models, combining search-and-score algorithms with EM and asymptotic approximations, demonstrated on synthetic and real data.

Contribution

It presents a novel feasible approach for structure and parameter learning in mixtures of DAGs, integrating interleaved search with EM and asymptotic model evaluation.

Findings

Effective on synthetic datasets

Successful application to real-world data

Outperforms simple search-and-score methods

Abstract

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.