Predicting User Activity Level In Point Processes With Mass Transport Equation

Point processes are powerful tools to model user activities and have a plethora of applications in social sciences. Predicting user activities based on point processes is a central problem. However, existing works are mostly problem specific, use heuristics, or simplify the stochastic nature of point processes. In this paper, we propose a framework that provides an efficient estimator of the probability mass function of point processes. In particular, we design a key reformulation of the prediction problem, and further derive a differential-difference equation to compute a conditional probability mass function. Our framework is applicable to general point processes and prediction tasks, and achieves superb predictive and efficiency performance in diverse real-world applications compared to the state of the art.