Speaker
Description
Ordinary differential equation models are central to systems biology and computational biology because they provide interpretable descriptions of regulatory, signaling and population-level dynamics \cite{ma}.
In many biological applications, however, longitudinal data are sparse, noisy, irregularly sampled and heterogeneous across individuals or experimental units. Classical nonlinear mixed-effects ODE models capture such heterogeneity, but rely on a fixed parametric vector field and can therefore be sensitive to model misspecification \cite{me}.
We present a Bayesian nonparametric mixed-effect ODE framework in which each subject is described by a shared population vector field together with an individual-specific deviation, both modeled with Gaussian process priors. Building on GP-ODE \cite{gpode} and Mixed-Effects GPs \cite{magma}, the proposed approach combines state-space trajectory priors with collocation-based ODE constraints, yielding tractable inference without repeated numerical ODE solves during training.
We evaluate the method on synthetic heterogeneous dynamical systems, including classical biological oscillators, and on real post-vaccination antibody kinetics data. The results show improved recovery of shared and subject-specific dynamics, better forecasting and adaptation to new subjects, and reliable uncertainty quantification, supporting the use of mixed-effect GP-ODEs as flexible data-driven dynamical models for heterogeneous biological systems.
Bibliography
@article{ma,
author = {Machado, Daniel and Costa, Rafael S. and Rocha, Miguel and Ferreira, Eug{\'e}nio C. and Tidor, Bruce and Rocha, Isabel},
title = {Modeling formalisms in systems biology},
journal = {AMB Express},
year = {2011},
volume = {1},
number = {1},
pages = {45}
}
@book{me,
author = {Lavielle, Marc},
title = {Mixed Effects Models for the Population Approach: Models, Tasks, Methods and Tools},
publisher = {Chapman and Hall/CRC},
year = {2014}
}
@inproceedings{gpode,
author = {Heinonen, Markus and Yildiz, Cagatay and Mannerstrom, Henrik and Intosalmi, Jukka and Lahdesmaki, Harri},
title = {Learning Unknown ODE Models with Gaussian Processes},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
year = {2018}
}
@article{magma,
author = {Arthur Leroy and Pierre Latouche and Benjamin Guedj and Servane Gey},
title = {{MAGMA}: inference and prediction using multi-task Gaussian processes with common mean},
journal = {Machine Learning},
year = {2022}
}
