arXiv：cs.LG· Julien Martinelli, Maksim Sinelnikov, Harri L\"ahdesm\"aki, Quentin Clairon, M\'elanie Prague·· 13 小时前
MEGPODE：基于高斯过程的贝叶斯非参数混合效应 ODE 模型
Bayesian Nonparametric Mixed-Effect ODEs with Gaussian Processes
AI 导读
研究者提出 MEGPODE，一种贝叶斯非参数混合效应 ODE 模型，将每个受试者的向量场分解为共享群体成分与个体偏差，两者均赋予高斯过程先验。该方法用状态空间 GP 先验表示隐轨迹，并在有限时间网格上惩罚其导数与向量场的差异，从而避免训练中反复求解 ODE，通过单一变分目标实现轨迹与向量场的近似联合推断。在异构振荡与生物医学 ODE 基准上，MEGPODE 的群体场恢复与个体轨迹预测均优于强基线。
正文
Abstract:Dynamical modelling in pharmacometrics, systems biology, and epidemiology often involves subjects with related but distinct dynamics, observed through temporally sparse and irregular measurements. Classical nonlinear mixed-effects ODE models represent this heterogeneity but rely on parametric vector fields, making them vulnerable to structural misspecification. Existing nonparametric ODE methods typically assume shared dynamics rather than an explicit mixed-effect hierarchy. We propose MEGPODE, a Bayesian nonparametric mixed-effect ODE model that decomposes each subject's vector field into a shared population component and a subject-specific deviation, both endowed with Gaussian process priors. To avoid repeated ODE solves during training, we represent latent trajectories with state-space GP priors and penalize discrepancies between their derivatives and the vector fields on a finite time grid. A single variational objective enables approximate joint inference over trajectories and vector fields, accounting for state uncertainty and dependence between population and subject-specific dynamics. Across heterogeneous oscillatory and biomedical ODE benchmarks, MEGPODE improves population-field recovery and subject-level trajectory prediction relative to strong baselines.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.13088 [cs.LG] |
| (or arXiv:2605.13088v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13088 arXiv-issued DOI via DataCite |
Submission history
From: Julien Martinelli [view email]
[v1]
Wed, 13 May 2026 06:57:01 UTC (1,656 KB)
[v2]
Fri, 9 Oct 2026 07:40:34 UTC (5,153 KB)
来源：arXiv：cs.LG · arxiv.org