Regression‐based network‐flow and inner‐matrix reconstruction

Network or matrix reconstruction is a general problem that occurs if the row‐ and column sums of a matrix are given, and the matrix entries need to be predicted conditional on the aggregated information. In this paper, we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on this equivalence, we extend the framework of network reconstruction, conditional on row and column sums, toward regression, which allows the inclusion of exogenous covariates and bootstrap‐based uncertainty quantification. More specifically, the mean of the regression model leads to the observed row and column margins. To exemplify the approach, we provide a simulation study and investigate interbank lending data, provided by the Bank for International Settlement. This dataset provides full knowledge of the real network and is, therefore, suitable to evaluate the predictions of our approach. It is shown that the inclusion of exogenous information leads to superior predictions in terms of L1 and L2 errors.