Modifying Bayesian Networks by Probability Constraints

TL;DR

This paper introduces algorithms to efficiently modify Bayesian networks to satisfy specific probability constraints while minimally altering their original distributions, using extended iterative proportional fitting procedures.

Contribution

It extends IPFP to Bayesian networks with E-IPFP and D-IPFP algorithms, enabling constraint satisfaction with reduced computational complexity.

Findings

Algorithms converge as proven theoretically.

Experiments confirm the algorithms' effectiveness.

Reduced computational cost demonstrated in experiments.

Abstract

This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only change its conditional probability tables, and the probability distribution of the resulting network should be as close as possible to that of the original network. We propose to 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. Limited analysis is provided, including the convergence proofs of the two algorithms. Computer experiments were conducted to validate the algorithms. The results are consistent with the theoretical analysis.