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Various privacy-preserving frameworks that respect the individual's privacyin the analysis of data have been developed in recent years. However, availablemodel classes such as simple statistics or generalized linear models lack theflexibility required for a good approximation of the underlying data-generatingprocess in practice. In this paper, we propose an algorithm for a distributed,privacy-preserving, and lossless estimation of generalized additive mixedmodels (GAMM) using component-wise gradient boosting (CWB). Making use of CWBallows us to reframe the GAMM estimation as a distributed fitting of baselearners using the $L_2$-loss. In order to account for the heterogeneity ofdifferent data location sites, we propose a distributed version of a row-wisetensor product that allows the computation of site-specific (smooth) effects.Our adaption of CWB preserves all the important properties of the originalalgorithm, such as an unbiased feature selection and the feasibility to fitmodels in high-dimensional feature spaces, and yields equivalent modelestimates as CWB on pooled data. Next to a derivation of the equivalence ofboth algorithms, we also showcase the efficacy of our algorithm on adistributed heart disease data set and compare it with state-of-the-artmethods.

Privacy-Preserving and Lossless Distributed Estimation of High-Dimensional Generalized Additive Mixed Models