F. J. Díez. Local conditioning in Bayesian networks. Artificial Intelligence, 87 (1996) 1-20.

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Local conditioning is an exact algorithm for computing probability in Bayesian networks, developed as an extension of Kim and Pearl's algorithm for singly-connected networks. A list of variables associated to each node guarantees that only the nodes inside a loop are conditioned on the variable which breaks it. The main advantage of this algorithm is that it computes the probability directly on the original network instead of building a cluster tree, and this can save time when debugging a model and when the sparsity of evidence allows a pruning of the network. The algorithm is also advantageous when some families in the network interact through AND/OR gates. A parallel implementation of the algorithm with a processor for each node is possible even in the case of multiply-connected networks.