Inferring Networks from Marginals Using Iterative Proportional Fitting

Serina Chang, Zhaonan Qu, Jure Leskovec, Johan Ugander

Keywords: network inference, dynamic graphs, iterative proportional fitting, Sinkhorn's algorithm

TL;DR: We establish a theoretical basis for using the iterative proportional fitting procedure to infer dynamic networks from their 3-dimensional marginals.

Abstract: When collecting dynamic network data, it is often more admissible—either due to privacy concerns or real-time feasibility—to collect the marginals of a network than its time-varying interiors. This reality, arising in classic and recent studies of human mobility, transportation, and migration networks, results in a natural and increasingly common network inference problem, where the goal is to infer a dynamic network from its 3-dimensional marginals, i.e., its time-varying rows, time-varying columns, and time-aggregated interaction matrix. Prior works on this problem have repurposed the popular iterative proportional fitting (IPF) procedure, also widely known as Sinkhorn’s algorithm, to infer dynamic networks from aggregate data; these resulting networks have been employed in several downstream tasks, including building tools for COVID-19 policymakers. Despite these high-impact applications, the behavior and assumptions of using IPF in this setting are not well understood. In this work, we fill in the missing theory, rigorously motivating the use of IPF for this network inference problem. Our main contribution is a statistical justification of the minimization principle of IPF for network inference, by formulating an instructive, generative network model whose maximum likelihood objective is dual to the Kullback-Leibler divergence minimization problem implied by IPF. Conveniently, the marginal observations form the sufficient statistics of the network model, aligning with problem constraints. We also run computational experiments with real-world mobility data, to demonstrate the effectiveness of IPF to infer networks in practice and to show how our new methods of analysis make it possible to inspect previously unstated assumptions.

Submission Type: Extended abstract (max 4 main pages).

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Submission Number: 119