Previous structural inference methods, such as NRI, fNRI and ACD, are good at eliminatingAU intheinference results. However,asshowninFigure 3,thesemethodsmayfalsely reconstruct the structure with indirect connections. Itisinteresting that the indirect connections resulted from the transmission of signals between nodes. However,this does not conform tothe future state prediction. Yet node1 can only affect node3 through node2, which results in a superposition of functions: f(f()). B.1 ImplementationdetailsofiSIDG We summarize the described architecture of iSIDG and present the pipeline of training iSIDG in Algorithm1.

In this paper, we propose a variational model, iterative Structural Inference of Directed Graphs (iSIDG), to infer the existence of directed interactions from observational agents' features over a time period in a dynamical system. First, the iterative process in our model feeds the learned interactions back to encourage our model to eliminate indirect interactions and to emphasize directional representation during learning. Second, we show that extra regularization terms in the objective function for smoothness, connectiveness, and sparsity prompt our model to infer a more realistic structure and to further eliminate indirect interactions. We evaluate iSIDG on various datasets including biological networks, simulated fMRI data, and physical simulations to demonstrate that our model is able to precisely infer the existence of interactions, and is significantly superior to baseline models.

In dynamical systems, the states of an agent are affected by the interactions, and the states are usually recorded as a set of continuous variables, which make it difficult to uncover the interactions based on the similarity between the agents.

In this paper, we propose a variational model, iterative Structural Inference of Directed Graphs (iSIDG), to infer the existence of directed interactions from observational agents' features over a time period in a dynamical system. First, the iterative process in our model feeds the learned interactions back to encourage our model to eliminate indirect interactions and to emphasize directional representation during learning. Second, we show that extra regularization terms in the objective function for smoothness, connectiveness, and sparsity prompt our model to infer a more realistic structure and to further eliminate indirect interactions. We evaluate iSIDG on various datasets including biological networks, simulated fMRI data, and physical simulations to demonstrate that our model is able to precisely infer the existence of interactions, and is significantly superior to baseline models.