标题： 一种用于网络分析的稀疏贝塔回归模型 显示英文标题

标题： A Sparse Beta Regression Model for Network Analysis

摘要： 对于网络数据的统计分析，$\beta$模型因其在结合节点异质性和理论可处理性方面的灵活性而成为一种有用的工具。 为了推广$\beta$模型，本文提出了稀疏$\beta$回归模型（S$\beta$RM），该模型结合了最近在建模相似性和稀疏性方面的两个研究主题。 具体而言，我们采用差异异质性，仅对重要节点分配权重，并提出带有$\ell_1$惩罚的惩罚似然函数用于参数估计。 虽然我们的估计方法与逻辑回归的 LASSO 方法密切相关，但我们发展了新的理论，强调使用我们的模型来处理通常在实践中看到的稀疏网络的参数范围。 更有趣的是，对相似性参数的推断不需要通常在 LASSO 类似估计中使用的去偏处理。 我们提供了广泛的模拟和数据分析来说明该模型的使用。 作为我们模型的一个特例，我们通过引入协变量扩展了 Erdős-Rényi 模型，并为稀疏网络开发了相关的统计推断，这可能具有独立的兴趣。 显示英文摘要

摘要： For statistical analysis of network data, the $\beta$-model has emerged as a useful tool, thanks to its flexibility in incorporating nodewise heterogeneity and theoretical tractability. To generalize the $\beta$-model, this paper proposes the Sparse $\beta$-Regression Model (S$\beta$RM) that unites two research themes developed recently in modelling homophily and sparsity. In particular, we employ differential heterogeneity that assigns weights only to important nodes and propose penalized likelihood with an $\ell_1$ penalty for parameter estimation. While our estimation method is closely related to the LASSO method for logistic regression, we develop new theory emphasizing the use of our model for dealing with a parameter regime that can handle sparse networks usually seen in practice. More interestingly, the resulting inference on the homophily parameter demands no debiasing normally employed in LASSO type estimation. We provide extensive simulation and data analysis to illustrate the use of the model. As a special case of our model, we extend the Erd\H{o}s-R\'{e}nyi model by including covariates and develop the associated statistical inference for sparse networks, which may be of independent interest.