Theoretical analysis and practical insights on importance sampling in Bayesian networks

Authors:
Changhe Yuan;Marek J. Druzdzel
Affiliations:
Department of Computer Science and Engineering, Mississippi State University, Mississippi State, MS 39762, United States;Decision Systems Laboratory, Intelligent Systems Program and School of Information Sciences, University of Pittsburgh, Pittsburgh, PA 15260, United States
Venue:
International Journal of Approximate Reasoning
Year:
2007

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Abstract

The AIS-BN algorithm [J. Cheng, M.J. Druzdzel, BN-AIS: An adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks, Journal of Artificial Intelligence Research 13 (2000) 155-188] is a successful importance sampling-based algorithm for Bayesian networks that relies on two heuristic methods to obtain an initial importance function: @e-cutoff, replacing small probabilities in the conditional probability tables by a larger @e, and setting the probability distributions of the parents of evidence nodes to uniform. However, why the simple heuristics are so effective was not well understood. In this paper, we point out that it is due to a practical requirement for the importance function, which says that a good importance function should possess thicker tails than the actual posterior probability distribution. By studying the basic assumptions behind importance sampling and the properties of importance sampling in Bayesian networks, we develop several theoretical insights into the desirability of thick tails for importance functions. These insights not only shed light on the success of the two heuristics of AIS-BN, but also provide a common theoretical basis for several other successful heuristic methods.