  Personalised federated learning (FL) aims at collaboratively learning a
machine learning model taylored for each client. Albeit promising advances have
been made in this direction, most of existing approaches works do not allow for
uncertainty quantification which is crucial in many applications. In addition,
personalisation in the cross-device setting still involves important issues,
especially for new clients or those having small number of observations. This
paper aims at filling these gaps. To this end, we propose a novel methodology
coined FedPop by recasting personalised FL into the population modeling
paradigm where clients' models involve fixed common population parameters and
random effects, aiming at explaining data heterogeneity. To derive convergence
guarantees for our scheme, we introduce a new class of federated stochastic
optimisation algorithms which relies on Markov chain Monte Carlo methods.
Compared to existing personalised FL methods, the proposed methodology has
important benefits: it is robust to client drift, practical for inference on
new clients, and above all, enables uncertainty quantification under mild
computational and memory overheads. We provide non-asymptotic convergence
guarantees for the proposed algorithms and illustrate their performances on
various personalised federated learning tasks.
