Approximate Inference for Infinite Contingent Bayesian Networks. Milch, B.; Marthi, B.; Sontag, D.; Russell, S.; Ong, D. L.; and 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   1 download  
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.
@inproceedings{MilchEtAl_aistats05,
 title = {Approximate Inference for Infinite Contingent {B}ayesian Networks},
 author = {Brian Milch and Bhaskara Marthi and David Sontag and Stuart Russell and Daniel L. Ong and Andrey Kolobov},
 booktitle = {Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics},
 year = {2005},
 pages = {238--245},
 keywords = {Machine learning},
 url_Paper = {http://people.csail.mit.edu/dsontag/papers/MilchEtAl_AIStats05.pdf},
 abstract = {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.}
}
% editor = {Robert G. Cowell and Zoubin Ghahramani},
% publisher = {Society for Artificial Intelligence and Statistics},
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