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A Variational Approximation for Analyzing the Dynamics of Panel Data.

Jurijs Nazarovs1,2, Rudrasis Chakraborty3, Songwong Tasneeyapant2

  • 1Department of Statistics, University of Wisconsin Madison.

Uncertainty in Artificial Intelligence : Proceedings of the ... Conference. Conference on Uncertainty in Artificial Intelligence
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Summary
This summary is machine-generated.

We introduce ME-NODE, a novel probabilistic model for analyzing longitudinal panel data. This mixed-effects model enhances understanding of childhood development and disease modeling by capturing hidden dynamics in patient measurements.

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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.