Local Information for Global Network Estimation in Latent Space Models

TL;DR

This paper introduces a method for estimating entire social networks from partial local information using a latent space model, addressing challenges of missing data and bias, with theoretical guarantees and practical demonstrations.

Contribution

It proposes a projected gradient descent algorithm for global network estimation from local partial data, with convergence guarantees and bias quantification.

Findings

The method achieves accurate network estimation with partial data.

Bias in local views can be quantified and mitigated.

Performance demonstrated on simulated and real social networks.

Abstract

In social networks, neighborhood is crucial for understanding individual behavior in response to environments, and thus it is essential to analyze an individual's local perspective within the global network. This paper studies how to utilize a partial information network centered around a given individual for global network estimation by fitting a general latent space model. Compared to the entire network, the partial information network contains a significant proportion of missing edges with its structure depending on a random, potentially sparse neighborhood, posing significant challenges for estimation. We address the challenges by proposing a projected gradient descent algorithm for maximizing the likelihood of the observed data and develop theoretical guarantees for its convergence under different neighborhood structures. Our convergence rates and estimation error bounds highlight the impact of bias in an individual's local view of the global network, and we further show that the bias can be quantified with an imbalance measure. Using simulated and real networks, we demonstrate the performance of our estimation method and how our approach enables researchers to gain additional insights into the structure of social networks, such as the tradeoff between degrees and imbalance.