This paper formulates and studies a novel algorithm for federated learning from large collections of local datasets. This algorithm capitalizes on an intrinsic network structure that relates the local datasets via an undirected empirical graph. We model such big data over networks using a networked linear regression model. Each local dataset has individual regression weights. The weights of close-knit sub-collections of local datasets are enforced to deviate only little. This lends naturally to a network Lasso problem which we solve using a primal-dual method. We obtain a distributed federated learning algorithm via a message passing implementation of this primal-dual method. We provide a detailed analysis of the statistical and computational properties of the resulting federated learning algorithm.
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