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Federated learning (FL) is emerging as a privacy-aware alternative toclassical cloud-based machine learning. In FL, the sensitive data remains indata silos and only aggregated parameters are exchanged. Hospitals and researchinstitutions which are not willing to share their data can join a federatedstudy without breaching confidentiality. In addition to the extreme sensitivityof biomedical data, the high dimensionality poses a challenge in the context offederated genome-wide association studies (GWAS). In this article, we present afederated singular value decomposition (SVD) algorithm, suitable for theprivacy-related and computational requirements of GWAS. Notably, the algorithmhas a transmission cost independent of the number of samples and is only weaklydependent on the number of features, because the singular vectors associatedwith the samples are never exchanged and the vectors associated with thefeatures only for a fixed number of iterations. Although motivated by GWAS, thealgorithm is generically applicable for both horizontally and verticallypartitioned data.

Federated singular value decomposition for high dimensional data