A Method of Learning Implication Networks from Empirical Data: Algorithm and Monte-Carlo Simulation-Based Validation

This paper describes an algorithmic means for inducing implication networks from empirical data samples. The induced network enables efficient inferences about the values of network nodes if certain observations are made. This implication induction method is approximate in nature as probablistic network requirements are relaxed in the construction of dependence relationships based on statistical testing. In order to examine the effectiveness and validity of the induction method, several Monte-Carlo simulations were conducted, where theoretical Bayesian networks were used to generate empirical data samples}some of which were used to induce implication relations, whereas others were used to verify the results of evidential reasoning with the induced networks. The values in the implication networks were predicted by applying a modified version of the Dempster-Shafer belief updating scheme. The results of predictions were, furthermore, compared to the ones generated by Pearl’s stochastic simulation method [21], a probabilistic reasoning method that operates directly on the theoretical Bayesian networks. The comparisons consistently show that the results of predictions based on the induced networks would be comparable to those generated by Pearl’s method, when reasoning in a variety of uncertain knowledge domains}those that were simulated using the presumed theoretical probabilistic networks of different topologies. Moreover, our validation experiments also reveal that the comparable performance of the implication-network-based-reasoning method can be achieved with much less computational cost than Pearl’s stochastic simulation method; specifically, in all our experiments, the ratio between the actual CPU time required by our method and that by Pearl’s is approximately 1:100.