Bayesian Inference of Online Social Network Statistics via Lightweight Random Walk Crawls

TL;DR

This paper introduces a Bayesian framework for reliable statistical inference of social network properties using lightweight random walk crawls, addressing the limitations of API-based data collection.

Contribution

It develops an unbiased estimator for network functions based on random walks and derives an approximate posterior distribution for Bayesian inference.

Findings

Estimator is unbiased and linked to spectral gap.

Bayesian inference provides credible estimates.

Validated on real-world social networks.

Abstract

Online social networks (OSN) contain extensive amount of information about the underlying society that is yet to be explored. One of the most feasible technique to fetch information from OSN, crawling through Application Programming Interface (API) requests, poses serious concerns over the the guarantees of the estimates. In this work, we focus on making reliable statistical inference with limited API crawls. Based on regenerative properties of the random walks, we propose an unbiased estimator for the aggregated sum of functions over edges and proved the connection between variance of the estimator and spectral gap. In order to facilitate Bayesian inference on the true value of the estimator, we derive the approximate posterior distribution of the estimate. Later the proposed ideas are validated with numerical experiments on inference problems in real-world networks.