在Template Model Builder（TMB）中实现神经网络混合效应模型（NMMs）

中文摘要 AI 辅助

神经网络混合效应模型（NMMs）结合了人工神经网络强大的表示与预测能力，以及混合效应建模捕捉复杂相关结构的能力，已获得广泛关注。然而，现有估计方法严重依赖手动推导目标函数和梯度，这必然需要进行简化近似，极大限制了NMMs的复杂性与准确性。本研究引入了一种使用Template Model Builder（TMB）实现NMMs的通用框架，通过利用自动微分和拉普拉斯近似，TMB仅要求用户指定负联合对数似然和任何正则化项。该框架会自动积分出随机效应，并评估边际目标函数及其精确梯度，无需手动推导或临时近似。我们通过两个数值示例展示了基于TMB的NMMs的效率、灵活性和统计性能，包括其在单调NMMs中的应用，还提供了可复现代码以促进更广泛的采用。

英文摘要

Neural network mixed-effects models (NMMs) have gained traction by combining the strong representation and predictive power of artificial neural networks with the capacity of mixed-effects modeling to capture complex correlation structures. However, existing estimation approaches rely heavily on manual derivations of objective functions and gradients, which inherently forces simplifying approximations and severely constrains the complexity and accuracy of NMMs. In this work, we introduce a general framework for implementing NMMs using Template Model Builder (TMB). By leveraging automatic differentiation and Laplace approximation, TMB requires users to specify only the negative joint log-likelihood and any regularization terms. The framework automatically integrates out random effects and evaluates the marginal objective function alongside its exact gradients, eliminating the need for manual derivations or ad hoc approximations. We demonstrate the efficiency, flexibility, and statistical performance of TMB-based NMMs across two numerical examples, including an application to monotonic NMMs. Reproducible code is provided to facilitate broader adoption.

发表机构

• Memorial University of Newfoundland（纽芬兰纪念大学）
• Alaska Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration（美国国家海洋和大气管理局国家海洋渔业服务处阿拉斯加渔业科学中心）
• Centre for Fisheries Ecosystems Research, Fisheries and Marine Institute of Memorial University of Newfoundland（纽芬兰纪念大学渔业与海洋学院渔业生态系统研究中心）

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