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**Being Bayesian about Network Structure**

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N. Friedman, and D. Koller.

In *Proc. Sixteenth Conf. on Uncertainty in Artificial Intelligence
(UAI)*, 2000.
Postscript version

PDF version.

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Abstract

In many domains, we are interested in analyzing the structure of the underlying
distribution, e.g., whether one variable is a direct parent of the other.
Bayesian model-selection attempts to find the MAP model and use 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 ordering over network variables. This allows us to compute,
for a given ordering, 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 an * Markov Chain Monte Carlo* (MCMC) method, but over orderings
rather than over network structures. The space of orderings is much
smaller and more regular than the space of structures, and has 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.

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