Popularity Regression-Based Latent Space Model for Large-Scale Sparse Network Analysis
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.
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BibTeX
@misc{gao2026popularity,
title = {{Popularity Regression-Based Latent Space Model for Large-Scale Sparse Network Analysis}},
author = {Zhan Gao and Danyang Huang and Rui Pan and Hansheng Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37284},
eprint = {2609.37284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37284},
}
RIS
TY - UNPB
TI - Popularity Regression-Based Latent Space Model for Large-Scale Sparse Network Analysis
AU - Zhan Gao
AU - Danyang Huang
AU - Rui Pan
AU - Hansheng Wang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37284
UR - https://arxiv.org/abs/2609.37284
AB - 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.
ER -