Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Approximating probabilistic inference in Bayesian belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
On the conversion between non-binary constraint satisfaction problems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Approximating Probabilistic Inference in Bayesian Belief Networks
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The Journal of Machine Learning Research
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The problem of counting the number of solutions to a constraint network (CN) (also called constraint satisfaction problems, CSPs) is rephrased in terms of probability updating in Bayes networks. Approximating the probabilities in Bayes networks is a problem which has been studied for a while, and may well provide a good approximation to counting the number of solutions. We use a simple approximation based on independence, and show that it is correct for tree‐structured CNs. For other CNs, it is less optimistic than a spanning‐tree approximation suggested in prior work. Experiments show that the Bayes nets estimation is more accurate on the average, compared to competing methods (the spanning‐tree, as well as a scheme based on a product of all compatible pairs of values). We present empirical evidence that our approximation may also be a useful (value ordering) search heuristic for finding a single solution to a constraint satisfaction problem.