Learning Deep Hidden Nonlinear Dynamics from Aggregate Data

Learning nonlinear dynamics from diffusion data is a challenging problem since the individ- uals observed may be different at different time points, generally following an aggregate be- haviour. Existing work cannot handle the tasks well since they model such dynamics either di- rectly on observations or enforce the availabil- ity of complete longitudinal individual-level trajectories. However, in most of the practical applications, these requirements are unrealis- tic: the evolving dynamics may be too complex to be modeled directly on observations, and individual-level trajectories may not be avail- able due to technical limitations, experimental costs and/or privacy issues. To address these challenges, we formulate a model of diffusion dynamics as the hidden stochastic process via the introduction of hidden variables for flexi- bility, and learn the hidden dynamics directly on aggregate observations without any require- ment for individual-level trajectories. We pro- pose a dynamic generative model with Wasser- stein distance for LEarninG dEep hidden Non- linear Dynamics (LEGEND) and prove its the- oretical guarantees as well. Experiments on a range of synthetic and real-world datasets il- lustrate that LEGEND has very strong perfor- mance compared to state-of-the-art baselines.