Network Inference: Nonparametric estimation, bootstrap, and model diagnostics in sparse graphon models with vertex attributes

网络推理：具有顶点属性的稀疏图形模型中的非参数估计、引导和模型诊断

• 批准号: 534099487
• 负责人: Professor Dr. Carsten Jentsch
• 金额: --
• 依托单位: Institut für Wirtschafts- und Sozialstatistik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/534099487?language=en
• 关键词: Network; Inference; Nonparametric; estimation; bootstrap

Statistical network analysis plays an important role in economics and social sciences as well as other research fields. In classical textbooks, many statistical and probabilistic aspects were discussed, and the statistical analysis of networks has been an active area of research since then. The main difficulties arise from the relational structure of networks which induces dependence, and from the fact that typically only one single network is observed. Asymptotic theory is therefore a greater challenge compared to classical data setups. This is true for many statistical tasks, but holds in particular when it comes to estimation, (bootstrap) inference, and model diagnostics. In this proposal, we tackle these problems by adopting a local dependence viewpoint: what happens “far apart” in the network may be treated as independent, and strong dependence appears only locally. We will address inference problems in models for network data with vertex attributes, which allows, e.g., to model interactions of people connected by social media with information about their workplace. We focus on models in which the networks are random. Our first specific goal is to develop a new graphon model which is suitable for modeling networks together with vertex attributes and study nonparametric as well as parametric estimation in this model. A focus in the estimation will be to avoid expensive discrete optimization and to achieve good convergence rates. Then, we study different bootstrap methods for networks. While the first bootstrap will be based on the new graphon model and allows the simultaneous resampling of a network together with vertex attributes, the second bootstrap under consideration is a block-type bootstrap for networks that borrows ideas from the configuration model to rewire the resampled sub-graphs, exploiting the idea of local dependence. We will study bootstrap consistency of both methods under various scenarios. Such results are crucial to develop valid inference methods. In particular, we will also study goodness-of-fit testing for graphon-type network models. We will consider online monitoring procedures for dynamic networks based on the previously mentioned graphon models. Finally, we are concerned with the estimation of counter-factual treatment effects from observational data with network interference. Hereby, we allow for peer and spill-over effects and focus on interventions that change the network structure, e.g., a lockdown, and we aim to avoid the often-made assumption of clustered interference or independent clusters. Throughout all workpackages of this project, we focus on two aspects: Firstly, developing rigorous theory and, secondly, providing accessible results and software for the specific models under consideration. On the one hand, this enables applied researchers to directly apply our methods to their data. On the other hand, our results can be used as starting point for further theoretical analysis in related models.

统计网络分析在经济学、社会科学以及其他研究领域中发挥着重要作用。在经典的教科书中，许多统计和概率方面的讨论，网络的统计分析一直是一个活跃的研究领域。主要的困难来自于网络的关系结构，它会导致依赖性，以及通常只观察到一个网络的事实。因此，与经典数据设置相比，渐近理论是一个更大的挑战。这对于许多统计任务来说都是正确的，但特别是在估计，（自举）推理和模型诊断方面。在这个建议中，我们通过采用局部依赖的观点来解决这些问题：网络中“相距甚远”的事情可以被视为独立的，强依赖性只出现在局部。我们将解决具有顶点属性的网络数据模型中的推理问题，例如，来模拟人们通过社交媒体与工作场所信息的互动。我们专注于网络是随机的模型。我们的第一个具体目标是开发一个新的图子模型，这是适合建模网络与顶点属性和研究非参数以及参数估计在这个模型中。在估计的重点将是避免昂贵的离散优化，并实现良好的收敛速度。然后，我们研究了不同的网络引导方法。虽然第一个引导程序将基于新的图子模型，并允许网络与顶点属性一起同时重采样，但考虑中的第二个引导程序是一个块型引导程序，用于网络，从配置模型中借用思想来重新布线重采样子图，利用局部依赖的思想。我们将研究这两种方法在不同场景下的自举一致性。这样的结果对于开发有效的推理方法至关重要。特别是，我们还将研究图子类型网络模型的拟合优度测试。我们将考虑基于前面提到的图子模型的动态网络的在线监控程序。最后，我们关注的是从具有网络干扰的观测数据中估计反事实治疗效果。因此，我们考虑到同伴效应和溢出效应，并专注于改变网络结构的干预措施，例如，一个锁定，我们的目标是避免集群干扰或独立集群的假设。在这个项目的所有工作包中，我们专注于两个方面：首先，开发严格的理论，其次，为正在考虑的特定模型提供可访问的结果和软件。一方面，这使应用研究人员能够直接将我们的方法应用于他们的数据。另一方面，我们的结果可以作为进一步的理论分析在相关模型的起点。