The M-DUCG methodology to calculate the joint probability distribution of directed cycle graph with local data and domain causal knowledge

Abstract

Modeling a complex system with a large number of variables at one time and collecting global data on a large scale is usually not practical. It is ideal to model the global system according to only local data and structures, and then synthesize them together. Multiple local structures can be easily synthesized as a global structure through fusing same nodes, while multiple sets of local data cannot be combined as the global data. Therefore, we need a method to obtain the joint probability distribution (JPD) of the global system by utilizing local data only. When the global structure synthesized does not include directed cyclic graph (DCG), it is easy to calculate the JPD with Bayesian network (BN). When DCGs are included, BN does not work. This paper presents the multi-valued Dynamic Uncertain Causality Graph (M-DUCG) methodology to calculate the global JPD in the case of DCGs with only local data. The idea is to use multiple sets of local data to learn the parameters of the synthesized M-DUCG structure with DCGs, and then use these parameters to calculate the global JPD.