Source localization, as a reverse problem of graph diffusion, is important for many applications such as rumor tracking, detecting computer viruses, and finding epidemic spreaders. However, it is still under-explored due to the inherent uncertainty of the diffusion process: after a long period of propagation, the same diffusion process may start with diverse sources. Most existing solutions utilize deterministic models and therefore cannot describe the diffusion uncertainty of sources. Moreover, current probabilistic approaches are hard to conduct smooth transformations with variational inference. To overcome the limitations, we propose a probabilistic framework using continuous normalizing flows with invertible transformations and graph neural networks to explicitly model the uncertainty of the diffusion source. Experimental results on two real-world datasets demonstrate the effectiveness of our model over strong baselines.

Discovering interesting yet unvisited point-of-interests (POIs) is among the most practical applications but challenging problems in location-based social networks (LBSNs). Popular approaches face several issues, such as data sparsity and difficulties in modeling latent nonlinearity between users and POIs. Furthermore, the uncertainty in LBSNs poses additional obstacles to learning good representations of users’ general and current interests. To effectively address these issues, we postulate that fusing multiple sources of information is paramount. Toward that, we propose a novel deep generative recommender system—Wasserstein autoencoder for POI recommendation (WaPOIR). It unifies the information from users’ personal preference, social influence, and geographical data, and captures users’ general interests from historical check-ins, while modeling users’ current interests from recently visited POIs. Unlike previous methods, WaPOIR learns the latent distribution of data in the Wasserstein space as a potential representation for each POI and each user in LBSNs. This enables simultaneous maintenance of social and POI interactions and modeling the uncertainty of their relationships. WaPOIR is a stochastic recommendation approach that allows Bayesian inference and approximation of variational posterior distribution. Extensive experiments conducted on real-world LBSN datasets demonstrate that WaPOIR achieves better performance over the state-of-the-art approaches.