One popular model for network analysis is the exchangeable graph model (ExGM), which is characterized by a two-dimensional function known as a graphon. Estimating an underlying graphon becomes the key of such analysis. Several nonparametric estimation methods have been proposed, and some are provably consistent. However, if certain useful features of the nodes (e.g., age and schools in a social network context) are available, none of these methods were designed to incorporate this source of information to help with the estimation. This paper develops a consistent graphon estimation method that integrates information from both the adjacency matrix itself and node features. We show that properly leveraging the features can improve the estimation. A cross-validation method is proposed to automatically select the tuning parameter of the method.

中文翻译：

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通过具有节点特征的graphon进行网络估计

一种流行的网络分析模型是可交换图模型 (ExGM)，其特征在于称为图子的二维函数。估计潜在的图形成为这种分析的关键。已经提出了几种非参数估计方法，其中一些方法可以证明是一致的。但是，如果节点的某些有用特征（例如，社交网络上下文中的年龄和学校）可用，则这些方法都没有设计为包含此信息源以帮助估计。本文开发了一种一致的图形估计方法，该方法集成了来自邻接矩阵本身和节点特征的信息。我们表明，适当利用这些特征可以改进估计。提出了一种交叉验证方法来自动选择该方法的调整参数。