Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Fusion and propagation with multiple observations in belief networks
Artificial Intelligence
On heuristics for finding loop cutsets in multiply-connected belief networks
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Pruning bayesian networks for efficient computation
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Symbolic probabilistic inference in belief networks
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
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This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian net is triangulated, this approach arranges its cliques into a tree and computes posterior probabilities by appropriately passing around messages in that tree. The computation in each clique is simply direct marginalization. When the underlying graph is not triangulated, one has to first triangulated it by adding edges. Referred to as the triangulation problem, the problem of finding an optimal or even a "good" triangulation proves to be difficult. In this paper, we propose to first decompose a Bayesian net into smaller components by making use of Tarjan's algorithm for decomposing an undirected graph at all its minimal complete separators. Then, the components are arranged into a tree and posterior probabilities are computed by appropriately passing around messages in that tree. The computation in each component is carried out by repeating the whole procedure from the ginning. Thus the triangulation problem is sidestepped.