Analysis of networks via the sparse β-model

• 成果类型: Article
• 署名作者: Chen, Mingli; Kato, Kengo; Leng, Chenlei
• 署名单位: University of Warwick; Cornell University; University of Warwick
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12444
• 发表日期: 2021
• 页码: 887-910
• 关键词: tuning parameter selection; Random graphs; stochastic blockmodels; diverging number; distributions; thresholds; inference

摘要

Data in the form of networks are increasingly available in a variety of areas, yet statistical models allowing for parameter estimates with desirable statistical properties for sparse networks remain scarce. To address this, we propose the Sparse beta-Model (S beta M), a new network model that interpolates the celebrated Erdos-Renyi model and the beta-model that assigns one different parameter to each node. By a novel reparameterization of the beta-model to distinguish global and local parameters, our S beta M can drastically reduce the dimensionality of the beta-model by requiring some of the local parameters to be zero. We derive the asymptotic distribution of the maximum likelihood estimator of the S beta M when the support of the parameter vector is known. When the support is unknown, we formulate a penalized likelihood approach with the l(0)-penalty. Remarkably, we show via a monotonicity lemma that the seemingly combinatorial computational problem due to the l0-penalty can be overcome by assigning non-zero parameters to those nodes with the largest degrees. We further show that a beta-min condition guarantees our method to identify the true model and provide excess risk bounds for the estimated parameters. The estimation procedure enjoys good finite sample properties as shown by simulation studies. The usefulness of the S beta M is further illustrated via the analysis of a microfinance take-up example.