Problem
Research questions and friction points this paper is trying to address.
Statistical inference for latent space network models
Theoretical analysis of maximum likelihood estimators
Generalization to dependent-edge and sparse scenarios
Statistical Inference on Latent Space Models for Network Data
🤖 AI Summary
Existing latent space models for networks primarily focus on point estimation and prediction, lacking a rigorous statistical framework for quantifying estimation uncertainty. Method: We develop the first unified theoretical framework establishing uniform consistency and asymptotic normality of the maximum likelihood estimator under general edge dependence structures and sparse network regimes—applicable to diverse edge types and link functions. Our approach integrates asymptotic statistical theory, uniform convergence analysis, and extensive simulation studies. Contribution/Results: This work extends latent space model inference beyond point estimation to enable principled confidence interval construction and hypothesis testing. It significantly enhances statistical reliability in downstream tasks such as link prediction and network comparison, providing a foundational basis for rigorous statistical inference on network data.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Maximum likelihood estimators for latent space models
Uniform consistency and asymptotic distribution analysis
Generalization to dependent-edge and sparse scenarios
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