Sampling and Inference for Large Networks

在“大数据”的当前景观中，大型网络（图）是普遍存在的对象，并且已经引起了很大的兴趣。 一个（社交）网络是一个复杂的关系图，由节点（参与者）和边（关系）组成，其中节点和边都可能有许多与之相关的属性（协变量）。 例子包括诸如Facebook的社交网络、引用和协作网络（诸如arXiv）、网络图（诸如维基百科）和通信网络。 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缘属性;以及它们如何随时间演变。 由于节点和边以及相关属性数据的绝对数量，这些大型网络的调查和分析可能会很困难。 研究人员面临的另一个困难是，前景是只有一个单一的观察网络，从其中获得估计。 本研究的总体目标是研究网络上的有效抽样方法，并使用频率论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，如基于排名的抽样技术和reservation技术，用于在分析整个网络在计算上不可行时对大型网络进行推断。 通过本研究，我计划至少培养三名硕士生和两名博士生。学生以及其他本科生。

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.