Being Bayesian about Network Structure

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 nonnegligible 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, bu...

• Type: Conference
• Year: 2000
• Where: UAI
• Authors: Nir Friedman, Daphne Koller
• Keywords: Bayesian Posterior, Posterior, Total Posterior Probability, UAI 2000, UAI 2008