A variational approximation for analyzing the dynamics of panel data
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:107-117, 2021.
Panel data involving longitudinal measurements of the same set of participants or entities taken over multiple time points is common in studies to understand early childhood development and disease modeling. Deep hybrid models that marry the predictive power of neural networks with physical simulators such as differential equations, are starting to drive advances in such applications. The task of modeling not just the observations/data but the hidden dynamics that are captured by the measurements poses interesting statistical/computational questions. We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing such panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms using MC based sampling methods and numerical ODE solvers. We demonstrate ME-NODE’s utility on tasks spanning the spectrum from simulations and toy datasets to real longitudinal 3D imaging data from an Alzheimer’s disease (AD) study, and study the performance for accuracy of reconstruction for interpolation, uncertainty estimates and personalized prediction.