Privacy-Preserved Evolutionary Graph Modeling via Gromov-Wasserstein Autoregression

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Real-world graphs like social networks are often evolutionary over time, whose observations at different timestamps lead to graph sequences. Modeling such evolutionary graphs is important for many applications, but solving this problem often requires the correspondence between the graphs at different timestamps, which may leak private node information, e.g., the temporal behavior patterns of the nodes. We proposed a Gromov-Wasserstein Autoregressive (GWAR) model to capture the generative mechanisms of evolutionary graphs, which does not require the correspondence information and thus preserves the privacy of the graphs' nodes. This model consists of two autoregressions, predicting the number of nodes and the probabilities of nodes and edges, respectively. The model takes observed graphs as its input and predicts future graphs via solving a joint graph alignment and merging task. This task leads to a fused Gromov-Wasserstein (FGW) barycenter problem, in which we approximate the alignment of the graphs based on a novel inductive fused Gromov-Wasserstein (IFGW) distance. The IFGW distance is parameterized by neural networks and can be learned under mild assumptions, thus, we can infer the FGW barycenters without iterative optimization and predict future graphs efficiently. Experiments show that our GWAR achieves encouraging performance in modeling evolutionary graphs in privacy-preserving scenarios.