PROJECTIVE, SPARSE AND LEARNABLE LATENT POSITION NETWORK MODELS

• 成果类型: Article
• 署名作者: Spencer, Neil A.; Shalizi, Cosma Rohilla
• 署名单位: University of Connecticut; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2340
• 发表日期: 2023
• 页码: 2506-2525
• 关键词: graphs

摘要

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the number of nodes, which is inappropriate when the graph is thought to be sparse. We propose an alternative assumption-that the latent positions are generated according to a Poisson point process-and show that it is compatible with various levels of sparsity. Unlike other notions of sparse latent position models in the literature, our framework also defines a projective sequence of probability models, thus ensuring consistency of statistical inference across networks of different sizes. We establish conditions for consistent estimation of the latent positions, and compare our results to existing frameworks for modeling sparse networks.