  We propose a novel federated learning paradigm to model data variability
among heterogeneous clients in multi-centric studies. Our method is expressed
through a hierarchical Bayesian latent variable model, where client-specific
parameters are assumed to be realization from a global distribution at the
master level, which is in turn estimated to account for data bias and
variability across clients. We show that our framework can be effectively
optimized through expectation maximization (EM) over latent master's
distribution and clients' parameters. We also introduce formal differential
privacy (DP) guarantees compatibly with our EM optimization scheme. We tested
our method on the analysis of multi-modal medical imaging data and clinical
scores from distributed clinical datasets of patients affected by Alzheimer's
disease. We demonstrate that our method is robust when data is distributed
either in iid and non-iid manners, even when local parameters perturbation is
included to provide DP guarantees. Moreover, the variability of data, views and
centers can be quantified in an interpretable manner, while guaranteeing
high-quality data reconstruction as compared to state-of-the-art autoencoding
models and federated learning schemes. The code is available at
https://gitlab.inria.fr/epione/federated-multi-views-ppca.
