Linking Micro Event History To Macro Prediction In Point Process Models

User behaviors in social networks are microscopic with fine grained temporal information. Predicting a macroscopic quantity based on users' collective behaviors is an important problem. However, existing works are mainly problem-specific models for the microscopic behaviors and typically design approximations or heuristic algorithms to compute the macroscopic quantity. In this paper, we propose a unifying framework with a jump stochastic differential equation model that systematically links the microscopic event data and macroscopic inference, and the theory to approximate its probability distribution. We showed that our method can better predict the user behaviors in real-world applications.