Learning Deep Hidden Nonlinear Dynamics from Aggregate Data

Understand

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour.

• Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availability of complete longitudinal individual-level trajectories.
• However, in most of the practical applications, these requirements are unrealistic: the evolving dynamics may be too complex to be modeled directly on observations, and individual-level trajectories may not be available due to technical limitations, experimental costs and/or privacy issues.
• To address these challenges, we formulate a model of diffusion dynamics as the {\em hidden stochastic process} via the introduction of hidden variables for flexibility, and learn the hidden dynamics directly on {\em aggregate observations} without any requirement for individual-level trajectories.