Importance sampling in Bayesian networks using probability trees

Abstract

In this paper a new Monte-Carlo algorithm for the propagation of probabilities in Bayesian networks is proposed. This algorithm has two stages: in the ÿrst one an approximate propagation is carried out by means of a deletion sequence of the variables. In the second stage a sample is obtained using as sampling distribution the calculations of the ÿrst step. The di erent conÿgurations of the sample are weighted according to the importance sampling technique. We show how the use of probability trees to store and to approximate probability potentials, and a careful selection of the deletion sequence, make this algorithm able to propagate over large networks with extreme probabilities.

Parallel Importance Sampling in Conditional Linear Gaussian Networks

“…zeros in the probability tables. In scenarios of extreme probabilities, EW is known to be not so accurate [16], and therefore more sophisticated methods as the ones proposed in [4] for mixtures of truncated exponentials, are to be developed.…”

New strategies for finding multiplicative decompositions of probability trees

“…A probability tree [1,5,14] is a directed labeled tree, where each internal node represents a variable and each leaf node represents a probability value. Each internal node has one outgoing arc for each state of the variable associated with that node.…”

“…functions representing probabilistic information). They are especially useful in contexts where large probability distributions are handled, being Bayesian networks a remarkable example [6,7,14].…”

Answering queries in hybrid Bayesian networks using importance sampling

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