论文标题
用于网络分析的稀疏beta回归模型
A Sparse Beta Regression Model for Network Analysis
论文作者
论文摘要
为了对网络数据进行统计分析，$β$ - 模型已成为有用的工具，这要归功于其在结合了鼻nodewise异质性和理论障碍方面的灵活性。为了概括$β$ - 模型，本文提出了稀疏的$β$ - 回归模型（S $β$ RM），该模型将最近在同质性和稀疏性建模方面开发了两个研究主题。特别是，我们采用差异异质性，仅将权重分配给重要节点，并提议以$ \ ell_1 $罚款进行惩罚的可能性，以进行参数估计。尽管我们的估计方法与逻辑回归的套索方法密切相关，但我们开发了新的理论，强调使用模型来处理可以处理通常在实践中看到的稀疏网络的参数制度。更有趣的是，对同质参数的推论要求在套索型估计中通常不使用任何偏见。我们提供广泛的仿真和数据分析，以说明模型的使用。作为我们模型的特殊情况，我们通过包括协变量并开发有关稀疏网络的相关统计推断，扩展了ERDőS-Rényi模型，这可能具有独立的兴趣。
For statistical analysis of network data, the $β$-model has emerged as a useful tool, thanks to its flexibility in incorporating nodewise heterogeneity and theoretical tractability. To generalize the $β$-model, this paper proposes the Sparse $β$-Regression Model (S$β$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 Erdős-Rényi model by including covariates and develop the associated statistical inference for sparse networks, which may be of independent interest.
