A method of learning implication networks from empirical data: algorithms and Monte Carlo simulation based validation

This paper describes an algorithmic method of inducing implication networks from empirical data samples and reports some validation results with this method. The induced network enables efficient inferences about the values of network nodes given certain observations. This implication induction method is approximate in nature as probabilistic network requirements are relaxed in the construction of dependence relationships based on statistical testing. In order to examine the validity of the induced networks, several Monte Carlo simulations were conducted where predefined 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 in the induced networks. The valves 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, a probabilistic reasoning method that operates directly on the predefined 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