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Being Bayesian about Bayesian Network Structure:A Bayesian Approach to Structure Discovery in Bayesian Networks. (2003)

by N. Friedman and D. Koller
[older version, 2000]

Abstract: In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior "landscape". We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.

Download Information

N. Friedman and D. Koller (2003). "Being Bayesian about Bayesian Network Structure:A Bayesian Approach to Structure Discovery in Bayesian Networks.." Machine Learning, 50(1--2), 95-125. Full version of UAI 2000 paper. pdf ps.gz

Bibtex citation

  author =       "N. Friedman and D. Koller",
  title =        "Being {Bayesian} about {Bayesian} Network Structure:
                 {A} {Bayesian} Approach to Structure Discovery in
                 {Bayesian} Networks.",
  journal =      "Machine Learning",
  volume  =  50,
  number = {1--2},
  pages = {95--125},
  year =         "2003",
  Note =  "Full version of UAI 2000 paper",

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