Learning Stochastic Behaviour of Aggregate Data

Learning nonlinear dynamics of aggregate data is a challenging problem since the full trajectory of each individual is not observable, namely, the individual observed at one time point may not be observed at next time point. One class of existing work investigate such dynamics by requiring complete longitudinal individual-level trajectories. However, in most of the practical applications, the requirement is unrealistic due to technical limitations, experimental costs and/or privacy issues. The other one class of methods learn the dynamics by regarding aggregate behaviour as a stochastic process with/without hidden variable. The performances of such methods may be restricted due to complex dynamics, high dimensions and computation costs. In this paper, we propose a new weak form based framework to study the hidden dynamics of aggregate data via Wasserstein generative adversarial network(WGAN) and Fokker Planck Equation(FPE). Our model fall into the second class of methods with simple structure and computation. We demonstrate our approach in the context of a series of synthetic and real-world datasets.