Popularity Regression-Based Latent Space Model for Large-Scale Sparse Network Analysis

2026-09-29

AI Summary

This study addresses the estimation challenges in latent space models for large-scale sparse networks arising from the interplay between degree heterogeneity and nodal feature dependence. To this end, it proposes a popularity-regression-based latent space model. Methodologically, four analytically tractable objective functions are constructed to accommodate complex dependency structures, while multiple estimators integrating both first- and higher-order network information are developed. Furthermore, rigorous asymptotic theory grounded in non-standard U-statistics is established, elucidating the distinct convergence rates among these estimators. Numerical simulations and link prediction experiments on an author-citation network demonstrate that the proposed approach achieves high-precision inference. Overall, this work provides a reliable theoretical and computational framework for the analysis of large-scale sparse networks.

Abstract

Degree heterogeneity is one of the most important properties of network data. It is widely observed that degree heterogeneity is often related to the nodal features. In this study, we investigate the estimation and statistical inference for a popularity regression-based latent space model with nodal features. Given the complex dependence structure induced by the latent space model, we aim to derive analytically tractable objective functions that effectively account for this structure for sparse networks. Specifically, we propose a total of four estimators. The first two estimators are developed by utilizing only the first-order structure of the network (e.g., the nodal degree), while the last two estimators are developed by leveraging the higher-order network structures (i.e., reciprocity and transitivity). Rigorous asymptotic theory is established based on various non-standard U-statistics. We find that different estimators might have different convergence rates. The extension to higher-order moments-based estimators is also discussed. Extensive numerical experiments and a real data analysis of link prediction for an author citation network are conducted for illustration purposes.

Problem

• Latent Space Model
• Sparse Network
• Degree Heterogeneity
• Popularity Regression
• Statistical Inference

Innovation

• Latent Space Model
• Popularity Regression
• Sparse Networks
• Non-standard U-statistics
• Degree Heterogeneity