Parametric Bootstrap on Networks with Non-Exchangeable Nodes

TL;DR

This paper develops a two-level parametric bootstrap method for networks modeled by Chung-Lu, addressing bias issues in uncertainty quantification for complex network statistics beyond node-exchangeable models.

Contribution

It introduces a bias-reducing two-level bootstrap procedure for non-exchangeable network models, extending classical bootstrap ideas to complex network settings.

Findings

Two-level bootstrap reduces bias in network uncertainty estimation

Method improves confidence interval accuracy for network statistics

Applicable to non-exchangeable network models like Chung-Lu

Abstract

This paper studies the parametric bootstrap method for networks to quantify the uncertainty of statistics of interest. While existing network resampling methods primarily focus on count statistics under node-exchangeable (graphon) models, we consider more general network statistics (including local statistics) under the Chung-Lu model without node-exchangeability. We show that the natural network parametric bootstrap that first estimates the network generating model and then draws bootstrap samples from the estimated model generally suffers from bootstrap bias. As a general recipe for addressing this problem, we show that a two-level bootstrap procedure provably reduces the bias. This essentially extends the classical idea of iterative bootstrap to the network setting with a growing number of parameters. Moreover, the second-level bootstrap provides a way to construct higher-accuracy confidence intervals for many network statistics.