Modifying Bayesian Networks by Probability Constraints

This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only changeing its conditional probability tables while keeping the probability distribution of the resulting network as close as possible to that of the original. We solve this problem by extending IPFP (iterative proportional fitting procedure) to probability distributions represented by Bayesian networks. The resulting algorithm, E-IPFP is further developed to D-IPFP, which reduces the computational cost by decomposing a global EIPFP into a set of smaller local E-IPFP problems. We provide a limited analysis, including the convergence proofs of the two algorithms. Computer experiments were conducted to validate the algorithms. The results are consistent with the theoretical analysis.