arXiv Machine Learning September 24, 2026 By Mohamed Tarek, Pedro Afonso

Fitting Large Nonlinear Mixed Effects Models Using Variational Expectation Maximization

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The paper introduces a scalable Variational Expectation Maximization (VEM) algorithm for fitting large Nonlinear Mixed Effects (NLME) models, addressing computational challenges that arise as parameter and random‑effect counts grow. VEM leverages flexible variational families and reverse‑mode automatic differentiation to efficiently maximize the marginal likelihood, enabling fitting of models with over 15,000 population parameters. Experiments using the Pumas software demonstrate VEM’s ability to improve log‑likelihood over many iterations while remaining computationally feasible, whereas traditional FOCE methods fail to complete even a single iteration for similarly sized models.

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