A Variational Approximation for Analyzing the Dynamics of Panel Data

Area of Science:

• Computational statistics
• Biomedical data science
• Machine learning for dynamical systems

Background:

• Longitudinal panel data are crucial for developmental and disease studies.
• Deep hybrid models combining neural networks and physical simulators show promise.
• Modeling hidden dynamics in longitudinal data presents statistical and computational challenges.

Purpose of the Study:

• To propose a probabilistic model, ME-NODE, for analyzing panel data with mixed effects.
• To leverage smooth approximations of Stochastic Differential Equations (SDEs) via the Wong-Zakai theorem.
• To develop efficient training algorithms for the proposed model.

Main Methods:

• Developed the ME-NODE probabilistic model incorporating fixed and random mixed effects.
• Utilized smooth approximations of SDEs based on the Wong-Zakai theorem.
• Derived Evidence Based Lower Bounds and employed Monte Carlo (MC) sampling and numerical ODE solvers for training.

Main Results:

• Demonstrated ME-NODE's effectiveness on simulated, toy, and real longitudinal 3D imaging data from an Alzheimer's disease (AD) study.
• Evaluated performance in terms of reconstruction accuracy for interpolation and uncertainty estimation.
• Showcased capabilities in personalized prediction for longitudinal studies.

Conclusions:

• ME-NODE provides a robust framework for analyzing complex longitudinal panel data.
• The model effectively captures underlying dynamics and offers accurate predictions.
• ME-NODE shows significant utility in applications like Alzheimer's disease research.