用变分期望最大化加速复杂药理模型拟合，支持超大规模参数。
Fitting Large Nonlinear Mixed Effects Models Using Variational Expectation Maximization
- 采用变分期望最大化算法，结合自动微分提升计算效率。
- 成功拟合含15410个群体参数的深层药代动力学模型。
- 适合需要高效处理高维随机效应的生物统计与药理研究者。
非线性混合效应模型（NLME）广泛用于药理学等领域分析分层纵向数据。但随着参数和随机效应数量增加，传统最大似然估计方法变得计算昂贵。本文探索变分期望最大化（VEM）算法，作为可扩展的替代方案。通过灵活的变分分布族和反向自动微分，VEM能高效最大化边缘似然，适用于含超过15,000个群体参数的NLME模型。研究详细描述了VEM方法，对比其与其他算法的表现，并通过计算实验验证其可扩展性。使用Pumas软件，分别拟合了标准华法林模型和含15,410个群体参数、16个随机效应的DeepNLME Friberg模型。华法林模型完成完整迭代以验证正确性，而DeepNLME模型仅运行有限迭代以测量每轮耗时并展示可扩展性。
原文摘要 · Abstract (English)
Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for maximizing the marginal likelihood become computationally expensive. This paper explores the Variational Expectation Maximization (VEM) algorithm, a scalable alternative for fitting NLME models. Originally introduced in the context of probabilistic graphical models and later popularized through variational autoencoders, VEM has not been extensively applied to NLME modeling. By leveraging flexible variational families and reverse-mode automatic differentiation, VEM can efficiently maximize the marginal likelihood, scaling to NLME models with over 15,000 population parameters. This work provides a detailed description of VEM, compares it to other NLME fitting algorithms, and highlights its scalability through computational experiments. Using the Pumas statistical software, we fit two test models: 1) a standard warfarin model, and 2) a DeepNLME Friberg model with 15,410 population parameters and 16 random effects. The warfarin model was fitted to completion to demonstrate the correctness of VEM, while the DeepNLME Friberg model was fitted for a limited number of iterations to measure the time per iteration and demonstrate VEM's scalability.
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