Simulation-based inference for stochastic nonlinear mixed-effects models with applications in systems biology

2025-04-15

AI Summary

Scalable Bayesian inference for multi-subject experimental data—such as mRNA transfection in systems biology—remains challenging due to high computational cost and model complexity. Method: We propose a hierarchical mixed-effects inference framework: first, amortized likelihood and posterior surrogates are constructed; then, subject-specific adaptation is performed via rapid fine-tuning. Crucially, we introduce a lightweight, neural-network-free Mixture-of-Experts (MoE) architecture that balances expressive power with interpretability and computational efficiency. The framework unifies simulation-based inference (SBI), amortized variational inference, and pseudo-marginal methods, and natively supports stochastic differential equation (SDE) models. Results: Experiments on real mRNA transfection data and complex SDEs demonstrate substantial speedups in inference while matching the statistical accuracy of exact pseudo-marginal approaches. The method enables efficient joint estimation of数十-dimensional parameter vectors across subjects.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes mixed-effects models widely applied in fields such as biology, pharmacokinetics, and sociology. In this work, we propose a novel methodology for scalable Bayesian inference in hierarchical mixed-effects models. Our framework first constructs amortized approximations of the likelihood and the posterior distribution, which are then rapidly refined for each individual dataset, to ultimately approximate the parameters posterior across many individuals. The framework is easily trainable, as it uses mixtures of experts but without neural networks, leading to parsimonious yet expressive surrogate models of the likelihood and the posterior. We demonstrate the effectiveness of our methodology using challenging stochastic models, such as mixed-effects stochastic differential equations emerging in systems biology-driven problems. However, the approach is broadly applicable and can accommodate both stochastic and deterministic models. We show that our approach can seamlessly handle inference for many parameters. Additionally, we applied our method to a real-data case study of mRNA transfection. When compared to exact pseudomarginal Bayesian inference, our approach proved to be both fast and competitive in terms of statistical accuracy.

Problem

• Scalable Bayesian inference for hierarchical mixed-effects models
• Amortized likelihood and posterior approximations for individual datasets
• Efficient parameter estimation in stochastic nonlinear systems biology models

Innovation

• Amortized likelihood and posterior approximations
• Mixtures of experts without neural networks
• Scalable Bayesian inference for hierarchical models