  As edge devices become increasingly powerful, data analytics are gradually
moving from a centralized to a decentralized regime where edge compute
resources are exploited to process more of the data locally. This regime of
analytics is coined as federated data analytics (FDA). In spite of the recent
success stories of FDA, most literature focuses exclusively on deep neural
networks. In this work, we take a step back to develop an FDA treatment for one
of the most fundamental statistical models: linear regression. Our treatment is
built upon hierarchical modeling that allows borrowing strength across multiple
groups. To this end, we propose two federated hierarchical model structures
that provide a shared representation across devices to facilitate information
sharing. Notably, our proposed frameworks are capable of providing uncertainty
quantification, variable selection, hypothesis testing and fast adaptation to
new unseen data. We validate our methods on a range of real-life applications
including condition monitoring for aircraft engines. The results show that our
FDA treatment for linear models can serve as a competing benchmark model for
future development of federated algorithms.
