Approximate Inference for Infinite Contingent Bayesian Networks. Milch, B., Marthi, B., Sontag, D., Russell, S., Ong, D. L., & Kolobov, A. In Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, pages 238–245, 2005.
Approximate Inference for Infinite Contingent Bayesian Networks [pdf]Paper  abstract   bibtex   
In many practical problems – from tracking aircraft based on radar data to building a bibliographic database based on citation lists – we want to reason about an unbounded number of unseen objects with unknown relations among them. Bayesian networks, which define a fixed dependency structure on a finite set of variables, are not the ideal representation language for this task. This paper introduces contingent Bayesian networks (CBNs), which represent uncertainty about dependencies by labeling each edge with a condition under which it is active. A CBN may contain cycles and have infinitely many variables. Nevertheless, we give general conditions under which such a CBN defines a unique joint distribution over its variables. We also present a likelihood weighting algorithm that performs approximate inference in finite time per sampling step on any CBN that satisfies these conditions.

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