In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: A BN20 network is a two level belief net in which parent interactions are modeled using the noisy-or interaction model. In this paper we discuss application of the SPI local expression language [1] to effi­ cient inference in large BN20 networks. In particular, we show that there is sig­ nificant structure which can be exploited to improve over the Quickscore result. We further describe how symbolic tech­ niques can provide information which can significantly reduce the computation required for computing all cause poste­ rior marginals. Finally, we present a novel approximation technique with pre­ liminary experimental results.

A: Symbolic Probabilistic Inference in large BN20 networks
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Q: There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their solutions. This paper introduces effective and compact, complete symmetry breaking constraints for small graph search. Enumerating with these symmetry breaks generates all and only non-isomorphic solutions. For small search problems, with up to 10 vertices, we compute instance independent symmetry breaking constraints. For small search problems with a larger number of vertices we demonstrate the computation of instance dependent constraints which are complete. We illustrate the application of complete symmetry breaking constraints to extend two known sequences from the OEIS related to graph enumeration.

A: Breaking Symmetries in Graph Search with Canonizing Sets
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Q: The belief network is a well-known graphi­ cal structure for representing independences in a joint probability distribution. The meth­ ods, which perform probabilistic inference in belief networks, often treat the conditional probabilities which are stored in the network as certain values. However, if one takes ei­ ther a subjectivistic or a limiting frequency approach to probability, one can never be certain of probability values. An algorithm should not only be capable of reporting the probabilities of the alternatives of remain­ ing nodes when other nodes are instanti­ ated; it should also be capable of reporting the uncertainty in these probabilities relative to the uncertainty in the probabilities which are stored in the network. In this paper a method for determining the variances in in­ ferred probabilities is obtained under the as­ sumption that a posterior distribution on the uncertainty variables can be approximated by the prior distribution. It is shown that this assumption is plausible if their is a reason­ able amount of confidence in the probabili­ ties which are stored in the network. Fur­ thermore in this paper, a surprising upper bound for the prior variances in the proba­ bilities of the alternatives of all nodes is ob­ tained in the case where the probability dis­ tributions of the probabilities of the alterna­ tives are beta distributions. It is shown that the prior variance in the probability at an al­ ternative of a node is bounded above by the largest variance in an element of the condi­ tional probability distribution for that node.

A:
Investigation of Variances in Belief Networks
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