Latent Point Process Models for Spatial-Temporal Networks

Social network data is generally incomplete with missing information about nodes and their interactions. Here we propose a spatial-temporal latent point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches, we assume that interactions are not fully observable, and certain interaction events lack information about participants. Instead, this information needs to be inferred from the available observations. We develop an efficient approximate algorithm based on variational expectation-maximization to infer unknown participants in an event given the location and the time of the event. We validate the model on synthetic as well as real-world data, and obtain very promising results on the identity-inference task. We also use our model to predict the timing and participants of future events, and demonstrate that it compares favorably with a baseline approach.