Network data are becoming increasingly available, and so there is a need to develop a suitable methodology for statistical analysis. Networks can be represented as graph Laplacian matrices, which are a type of manifold‐valued data. Our main objective is to estimate a regression curve from a sample of graph Laplacian matrices conditional on a set of Euclidean covariates, for example, in dynamic networks where the covariate is time. We develop an adapted Nadaraya–Watson estimator which has uniform weak consistency for estimation using Euclidean and power Euclidean metrics. We apply the methodology to the Enron email corpus to model smooth trends in monthly networks and highlight anomalous networks. Another motivating application is given in corpus linguistics, which explores trends in an author's writing style over time based on word co‐occurrence networks.

中文翻译：

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网络的非参数回归

网络数据变得越来越可用，因此需要开发一种合适的统计分析方法。网络可以表示为图拉普拉斯矩阵，它是流形值数据的一种。我们的主要目标是从以一组欧几里得协变量为条件的图拉普拉斯矩阵样本中估计回归曲线，例如，在协变量为时间的动态网络中。我们开发了一种经过改编的Nadaraya–Watson估计量，该估计量具有一致的弱一致性，可用于使用欧几里得和幂次欧几里得度量进行估计。我们将该方法应用于Enron电子邮件语料库，以对月度网络中的平滑趋势进行建模并突出显示异常网络。语料库语言学还提供了另一个激励性的应用，它探讨了作者语言的发展趋势。