Figure 1

Granger causality and Bayesian network inference approaches applied on a simple linear toy model. A. Five time series are simultaneously generated, and the length of each time series is 1000. X₂, X₃, X₄ and X₅ are shifted upward for visualization purpose. B. Granger causality results. (a) The network structure inferred from Granger causality approach. (b) The 95% confidence intervals graph for all the possible directed connections. (c) For visualization purpose, all directed edges (causalities) are sorted and enumerated into the table. The total number of edges is 20. C. Dynamic Bayesian network inference results. (a) The causal network structure learned from Bayesian network inference. (b) Each variable is represented by four nodes, representing different time-lags, we have a total of 20 nodes. They are numbered and enumerated in the table. (c) The simplified network structure: since we only care about the causality to the current time status, we can remove all the other edges and nodes that have no connection to the node 16 to node 20 (five variables with current time status). (d). A further simplified network structure of causality.