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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<jats:inline-formula><jats:alternatives><jats:tex-math>$$L_2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>L<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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.<\/jats:p>","DOI":"10.1007\/s11222-023-10323-2","type":"journal-article","created":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T11:02:07Z","timestamp":1699354927000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Privacy-preserving and lossless distributed estimation of high-dimensional generalized additive mixed models"],"prefix":"10.1007","volume":"34","author":[{"given":"Schalk","family":"Daniel","sequence":"first","affiliation":[]},{"given":"Bischl","family":"Bernd","sequence":"additional","affiliation":[]},{"given":"R\u00fcgamer","family":"David","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,7]]},"reference":[{"issue":"104","key":"10323_CR1","first-page":"008","volume":"127","author":"MM Anjum","year":"2022","unstructured":"Anjum, M.M., Mohammed, N., Li, W., et al.: Privacy preserving collaborative learning of generalized linear mixed model. 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