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.
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