Fitting Large Nonlinear Mixed Effects Models Using Variational Expectation Maximization
This work addresses the high computational cost of traditional methods for fitting high-dimensional nonlinear mixed-effects (NLME) models by introducing, for the first time, a systematic application of the variational expectation-maximization (VEM) algorithm to NLME modeling. By combining flexible variational distribution families with reverse-mode automatic differentiation, the proposed approach efficiently maximizes the marginal likelihood. The method substantially enhances the scalability of large-scale NLME models, demonstrating both correctness—validated on the standard warfarin model—and exceptional computational efficiency and scalability when applied to the DeepNLME Friberg model with 15,410 population parameters, thereby overcoming performance bottlenecks inherent in existing algorithms.