Various privacy-preserving frameworks that respect the individual's privacy in the analysis of data have been developed in recent years. However, available model classes such as simple statistics or generalized linear models lack the flexibility required for a good approximation of the underlying data-generating process in practice. In this paper, we propose an algorithm for a distributed, privacy-preserving, and lossless estimation of generalized additive mixed models (GAMM) using component-wise gradient boosting (CWB). Making use of CWB allows us to reframe the GAMM estimation as a distributed fitting of base learners using the $L_2$-loss. In order to account for the heterogeneity of different data location sites, we propose a distributed version of a row-wise tensor product that allows the computation of site-specific (smooth) effects. Our adaption of CWB preserves all the important properties of the original algorithm, such as an unbiased feature selection and the feasibility to fit models in high-dimensional feature spaces, and yields equivalent model estimates as CWB on pooled data. Next to a derivation of the equivalence of both algorithms, we also showcase the efficacy of our algorithm on a distributed heart disease data set and compare it with state-of-the-art methods.

翻译：近年来，为在数据分析中尊重个人隐私，各类隐私保护框架得以发展。然而，现有的模型类别（如简单统计量或广义线性模型）缺乏在实际场景中对潜在数据生成过程进行良好近似所需的灵活性。本文提出了一种基于分量梯度提升（CWB）的分布式、隐私保护且无损的广义加性混合模型（GAMM）估计算法。利用CWB，我们将GAMM估计重构为基于$L_2$损失的基础学习器分布式拟合问题。为解决不同数据站点间的异质性，我们提出了一种行式张量积的分布式版本，从而支持计算站点特定的（平滑）效应。本文对CWB的改编保留了原始算法的所有重要特性，例如无偏特征选择及在高维特征空间中拟合模型的能力，并能够得到与基于合并数据的CWB等价的模型估计值。除了推导两种算法的等价性，我们还通过分布式心脏病数据集展示了算法的有效性，并将其与现有最优方法进行了比较。