A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn’s algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF’s parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.

Federated learning (FL) learns a model jointly from a set of participating devices without sharing each other’s privately held data. The characteristics of non-i.i.d. data across the network, low device participation, high communication costs, and the mandate that data remain private bring challenges in understanding the convergence of FL algorithms, particularly regarding how convergence scales with the number of participating devices. In this paper, we focus on Federated Averaging (FedAvg), one of the most popular and effective FL algorithms in use today, as well as its Nesterov accelerated variant, and conduct a systematic study of how their convergence scale with the number of participating devices under non-i.i.d. data and partial participation in convex settings. We provide a unified analysis that establishes convergence guarantees for FedAvg under strongly convex, convex, and overparameterized strongly convex problems. We show that FedAvg enjoys linear speedup in each case, although with different convergence rates and communication efficiencies. For strongly convex and convex problems, we also characterize the corresponding convergence rates for the Nesterov accelerated FedAvg algorithm, which are the first linear speedup guarantees for momentum variants of FedAvg in convex settings. Empirical studies of the algorithms in various settings have supported our theoretical results.