# Statistical Inference on Latent Space Models for Network Data

arXiv: https://arxiv.org/abs/2312.06605 · HTML: https://mlsanity.com/paper/2312.06605/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2023.

## Built on by (most cited first, 4 of 4)

- [Representation-Enhanced Neural Knowledge Integration with Application to Large-Scale Medical Ontology Learning](https://mlsanity.com/paper/2410.07454/) (2024)
- [Nonparametric learning of heterogeneous graphical model on network-linked data](https://mlsanity.com/paper/2507.01473/) (2025)
- [Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation](https://mlsanity.com/paper/2605.05446/) (2026)
- [Efficient Synthetic Network Generation via Latent Embedding Reconstruction](https://mlsanity.com/paper/2606.00934/) (2026)

## Abstract (arXiv)

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on point estimation and prediction, leaving the statistical inference of latent space models an open question. This work aims to fill this gap by providing a general framework to analyze the theoretical properties of the maximum likelihood estimators. In particular, we establish the uniform consistency and asymptotic distribution results for the latent space models under different edge types and link functions. Furthermore, the proposed framework enables us to generalize our results to the dependent-edge and sparse scenarios. Our theories are supported by simulation studies and have the potential to be applied in downstream inferences, such as link prediction and network testing problems.