Sampling and Inference for Large Networks

在当前的“大数据”环境中，大型网络（图）是无处不在的对象，引起了人们的极大兴趣。（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许多与之相关的属性（协变量）。例子包括社交网络，如Facebook，引文和协作网络（如arXiv），网络图表（如维基百科）和通信网络。研究人员感兴趣的是网络结构和关系的建模，以及它们如何依赖于节点和边缘属性；以及它们是如何随时间进化的。由于节点和边缘以及相关属性数据的数量庞大，对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，只能从一个观察到的网络中获得估计。本研究的总体目标是研究网络上的有效采样方法，并研究使用频率和贝叶斯方法基于样本的网络模型的参数和非参数推理。

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.