Privacy-preserving federated tensor decomposition of single-cell immune data: recovering multicellular programs across institutions

Tensor decomposition of donor $\times$ cell-type $\times$ gene single-cell data recovers \emph{multicellular programs}: coordinated axes of inter-individual transcriptional variation that span cell types and stratify disease. Yet immune single-cell atlases are increasingly multi-institution, multi-ancestry, and governed, so patient cells often cannot be pooled. We present a federated estimator: each site computes a local program subspace, and a coordinator merges these by stacked SVD under federated global-mean centering, provably equivalent (up to truncation) to the centralised decomposition. This centering makes the merge robust to site-label confounding (program AUC $0.957$ vs.\ $0.861$ for naive per-site centering). Only program subspaces leave a site, and aggregation is compatible with secure aggregation. On a 261-donor systemic lupus erythematosus atlas it recovers the canonical interferon program (ISG enrichment AUC $0.998$; case--control separation $0.958$; bootstrap $Δ\text{AUC}=-0.000$, 95\% CI $[-0.004,+0.012]$ vs.\ centralised), across institution-scale and multi-ancestry partitions, and across three \emph{real} COVID-19 sites (subspace correlation $0.989$). It recovers the program when \emph{no site observes all cell types} (correlation $1.000$, exact by construction), which fixed-feature federated PCA cannot. On an interstitial-lung-disease atlas the recovered program predicts disease better than the best single cell type (AUC $0.96$ vs.\ $0.91$; gap 95\% CI excludes zero) and the advantage survives federation; a liver cohort is consistent ($p=0.005$). Membership-inference shows secure aggregation cuts attack AUC from $0.91$ to $0.61$. The method enables cross-institution, cross-ancestry recovery of multicellular immune programs without sharing cells.

Federated Block-Term Tensor Regression for decentralised data analysis in healthcare

Block-Term Tensor Regression (BTTR) has proven to be a powerful tool for modeling complex, high-dimensional data by leveraging multilinear relationships, making it particularly well-suited for applications in healthcare and neuroscience. However, traditional implementations of BTTR rely on centralized datasets, which pose significant privacy risks and hinder collaboration across institutions. To address these challenges, we introduce Federated Block-Term Tensor Regression (FBTTR), an extension of BTTR designed for federated learning scenarios. FBTTR enables decentralized data analysis, allowing institutions to collaboratively build predictive models while preserving data privacy and complying with regulations. FBTTR represents a major step forward in applying tensor regression to federated learning environments. Its performance is evaluated in two case studies: finger movement decoding from Electrocorticography (ECoG) signals and heart disease prediction. In the first case study, using the BCI Competition IV dataset, FBTTR outperforms non-multilinear models, demonstrating superior accuracy in decoding finger movements. For the dataset, for subject 3, the thumb obtained a performance of 0.76 $\pm$ .05 compared to 0.71 $\pm$ 0.05 for centralised BTTR. In the second case study, FBTTR is applied to predict heart disease using real-world clinical datasets, outperforming both standard federated learning approaches and centralized BTTR models. In the Fed-Heart-Disease Dataset, an AUC-ROC was obtained of 0.872 $\pm$ 0.02 and an accuracy of 0.772 $\pm$ 0.02 compared to 0.812 $\pm$ 0.003 and 0.753 $\pm$ 0.007 for the centralized model.