Sampling and Inference for Large Networks

在当前的大数据版图中，大型网络(图)是无处不在的对象，吸引了很多人的兴趣。(社会)网络是由节点(参与者)和边(关系)组成的复杂关系图，其中节点和边都可能具有与它们相关联的多个属性(协变量)。例子包括Facebook等社交网络、引用和协作网络(如arxiv)、网络图表(如维基百科)和交流网络。研究人员感兴趣的是对网络结构和关系进行建模，以及这些结构和关系如何依赖于节点和边的属性；以及它们可能随着时间的推移而演变。由于节点和边的绝对数量以及相关的属性数据，对这些大型网络的调查和分析可能会被证明是困难的。研究人员面临的另一个困难是，可能只有一个单一的观测网络来获得估计。这项研究的总体目标是研究网络上的有效抽样方法，并使用频域方法和贝叶斯方法研究基于样本的网络模型的参数和非参数推断。 具体的计划目标包括研究特定的抽样技术，如基于排序的抽样技术和重抽样技术，以便在分析整个网络时做出关于大型网络的推断在计算上不可行。通过这项研究，我计划培养至少三名硕士。学生和两名博士生以及固定本科生。

In the current landscape of "Big Data", large networks (graphs) are pervasive objects and have attracted much interest. A (social) network is a complex relational graph consisting of nodes (actors) and edges (relations), where both nodes and edges may have a number of attributes (covariates) associated with them. Examples include social networks such as Facebook, citation and collaboration networks (such as arXiv), web graphs (such as Wikipedia) and communication networks. Researchers are interested in modelling network structures and relations, as well as how these depend on the node and edge attributes; and, possibly, how they evolve over time. The investigation and analysis of these large networks can prove difficult due to the sheer number of nodes and edges and associated attribute data. Another difficulty that researchers are faced with is the prospect of having only a single observed network from which estimates are obtained. The general objectives for this research are to investigate efficient sampling methods on networks and to investigate both parametric and nonparametric inference for network models based on samples using both frequentist and Bayesian methods. Specific program objectives include research on specific sampling techniques, such as ranked based sampling techniques and resampling techniques, for making inferences about large networks when analyzing the whole network is not computationally feasible. Through this research, I plan to train at least three M.Sc. students and two Ph.D. students as well as fixe undergraduate students.