Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Thin junction tree filters for simultaneous localization and mapping
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Utilizing knowledge-base semantics in graph-based algorithms
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
A graph-theoretic analysis of information value
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Incremental compilation of bayesian networks
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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The undirected technique for evaluating belief networks [Jensen et al., 199Oa, Lauritzen and Spiegelhalter, 1988] requires clustering the nodes in the network into a junction tree. In the traditional view, the junction tree is constructed from the cliques of the moralized and triangulated belief network: triangulation is taken to be the primitive concept, the goal towards which any clustering algorithm (e.g. node elimination) is directed. In this paper, we present, an alternative conception of clustering, in which clusters and the junction tree property play the role of primitives: given a graph (not a tree) of clusters which obey (a modified version of) the junction tree property, we transform this graph until we have obtained a tree. There are several advantages to this approach: it is much clearer and easier to understand, which is important for humans who are constructing belief networks; it admits a wider range of heuristics which may enable more efficient or superior clustering algorithms; and it serves as the natural basis for an incremental clustering scheme, which we describe.