Are Extreme Value Estimation Methods Useful for Network Data?

TL;DR

This paper explores the use of extreme value theory for semi-parametric estimation of network degree distributions, offering robustness over traditional parametric methods especially with complex or corrupted data.

Contribution

It introduces a semi-parametric approach focusing on high-degree nodes using extreme value theory, improving robustness in network parameter estimation.

Findings

Semi-parametric method outperforms parametric models with corrupted data.

Extreme value approach provides more reliable estimates in model misspecification.

Method effectively captures tail behavior of degree distributions.

Abstract

Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However, there are often limitations in fitting parametric network models to data due to the complex nature of real-world networks. In this paper, we consider a semi-parametric estimation approach by looking at only the nodes with large in- or out-degrees of the network. This method examines the tail behavior of both the marginal and joint degree distributions and is based on extreme value theory. We compare it with the existing parametric approaches and demonstrate how it can provide more robust estimates of parameters associated with the network when the data are corrupted or when the model is misspecified.