Network Regression and Supervised Centrality Estimation

The centrality in a network is often used to measure nodes’ importance and model network effects on a certain outcome. Empirical studies widely adopt a two-stage procedure, which first estimates the centrality from the observed noisy network and then infers the network effect from the estimated centrality, even though it lacks theoretical understanding. We propose a unified modeling framework, under which we first prove the shortcomings of the two-stage procedure, including the inconsistency of the centrality estimation and the invalidity of the network effect inference. Furthermore, we propose a supervised centrality estimation methodology, which aims to simultaneously estimate both centrality and network effect. The advantages in both regards are proved theoretically and demonstrated numerically via extensive simulations and a case study in predicting currency risk premiums from the global trade network. The visit of Prof Haipeng Shen is part of the activities of the PRIN research project CoEnv - Complex Environmental Data and Modeling, funded by the Italian Ministry for University and Research and by the NextGenerationEU programme of the European Union.