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.
Highlights
We know that directed acyclic graphs (DAGs) can represent the joint probability distribution (JPD) of a set of random variables X1, X2...Xn, and this JPD can be factorized as the multiplication of a set of conditional probabilities as shown in equation (1).Pr(x1, x2, xn ) Pr(xi | pa(xi )) (1) iIn (1), xi is an instance of Xi, pa(xi) denotes the instances of the parent variables of xi, Pr(xi|pa(xi)) denotes the conditional probability of xi
Modules allow directed cyclic graph (DCG) when they are fused as a global system, while family can only be used for DAGs
With the same local data, the results of Gibbs sampling and MDUCG are very close in trend, only a few point have big gap, but as the number of sampling increases, the sampling curve is getting closer to the multi-valued Dynamic Uncertain Causality Graph (M-dynamic uncertain causality graph model (DUCG)) curve
Summary
We know that directed acyclic graphs (DAGs) can represent the JPD of a set of random variables X1, X2...Xn, and this JPD can be factorized as the multiplication of a set of conditional probabilities as shown in equation (1). It is found that such obtained marginal probability is not equal to that resulted from the marginal calculation according to JPD in the case with DCGs. Secondly, since the premise of probability calculation is logical operation in M-DUCG, the logical expression needs to be obtained first by expanding and simplifying, and calculate the corresponding probability with parameters. THE PROBABILITY EXPRESSION OF M-DUCG Since Fig. is a DCG, BN is unable to calculate its JPD, even though there are raw data belong to modules in Fig.. We can further expand (7) as while applying assumption 41 [23] to discard logic cycles
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
