  Federated learning allows for the training of machine learning models on
multiple decentralized local datasets without requiring explicit data exchange.
However, data pre-processing, including strategies for handling missing data,
remains a major bottleneck in real-world federated learning deployment, and is
typically performed locally. This approach may be biased, since the
subpopulations locally observed at each center may not be representative of the
overall one. To address this issue, this paper first proposes a more consistent
approach to data standardization through a federated model. Additionally, we
propose Fed-MIWAE, a federated version of the state-of-the-art imputation
method MIWAE, a deep latent variable model for missing data imputation based on
variational autoencoders. MIWAE has the great advantage of being easily
trainable with classical federated aggregators. Furthermore, it is able to deal
with MAR (Missing At Random) data, a more challenging missing-data mechanism
than MCAR (Missing Completely At Random), where the missingness of a variable
can depend on the observed ones. We evaluate our method on multi-modal medical
imaging data and clinical scores from a simulated federated scenario with the
ADNI dataset. We compare Fed-MIWAE with respect to classical imputation
methods, either performed locally or in a centralized fashion. Fed-MIWAE allows
to achieve imputation accuracy comparable with the best centralized method,
even when local data distributions are highly heterogeneous. In addition,
thanks to the variational nature of Fed-MIWAE, our method is designed to
perform multiple imputation, allowing for the quantification of the imputation
uncertainty in the federated scenario.
