Regression-Based Network Reconstruction

Network (or matrix) reconstruction is a general problem that occurs if the marginsof a matrix are given and the matrix entries need to be predicted. 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 restrictedmaximum likelihood estimation relying on augmented Lagrangian optimization.Based on the equivalence we extend the framework of network reconstruction towardsregression by allowing for exogenous covariates and random heterogeneityeffects. To exemplify the approach we look at interbank lending data, provided bythe Bank for International Settlement (BIS). This dataset provides full knowledgeof 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 superiorpredictions in terms of L1 and L2 errors. We compare prediction properties tocompeting algorithms and suggest a bootstrap approach to assess uncertainty