Network regression and supervised centrality estimation

TL;DR

This paper introduces a unified framework for centrality estimation and network regression with noisy data, proposing a supervised method that improves accuracy over traditional two-stage procedures, demonstrated through simulations and a real-world case study.

Contribution

It develops a novel supervised centrality estimation approach that jointly estimates centrality and network effects, addressing limitations of existing two-stage methods.

Findings

Supervised method outperforms two-stage approach in accuracy.

Theoretical analysis confirms improved estimation properties.

Case study demonstrates practical effectiveness in financial network analysis.

Abstract

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 to study the properties of centrality estimation and inference and the subsequent network regression analysis with noisy network observations. Furthermore, we propose a supervised centrality estimation methodology, which aims to simultaneously estimate both centrality and network effect. We showcase the advantages of our method compared with the two-stage method both theoretically and numerically via extensive simulations and a case study in predicting currency risk premiums from the global trade network.