Annealed importance sampling for structure learning in Bayesian networks

Authors:
Teppo Niinimäki;Mikko Koivisto
Affiliations:
HIIT & Department of Computer Science, University of Helsinki, Finland;HIIT & Department of Computer Science, University of Helsinki, Finland
Venue:
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Year:
2013

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Abstract

We present a new sampling approach to Bayesian learning of the Bayesian network structure. Like some earlier sampling methods, we sample linear orders on nodes rather than directed acyclic graphs (DAGs). The key difference is that we replace the usual Markov chain Monte Carlo (MCMC) method by the method of annealed importance sampling (AIS). We show that AIS is not only competitive to MCMC in exploring the posterior, but also superior to MCMC in two ways: it enables easy and efficient parallelization, due to the independence of the samples, and lower-bounding of the marginal likelihood of the model with good probabilistic guarantees. We also provide a principled way to correct the bias due to order-based sampling, by implementing a fast algorithm for counting the linear extensions of a given partial order.