Inference for graphs and networks: Extending classical tools to modern data

TL;DR

This paper introduces a unified statistical framework for network inference, extending classical tools to analyze large-scale graph and network data, with a focus on hypothesis testing and identifying key statistical challenges.

Contribution

It develops a generalized likelihood ratio approach for network hypothesis testing and highlights the need for new statistical methods tailored to large-scale network data.

Findings

Framework for hypothesis testing in networks using likelihood ratios

Identification of key statistical challenges in large-scale network inference

Call for strong contributions from statistical science to advance the field

Abstract

Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been eagerly adopted by practitioners in the service of network inference, they do not yet comprise a unified and coherent framework for the statistical analysis of large-scale network data. This paper serves as both an introduction to the topic and a first step toward formal inference procedures. We develop and illustrate our arguments using the example of hypothesis testing for network structure. We invoke a generalized likelihood ratio framework and use it to highlight the growing number of topics in this area that require strong contributions from statistical science. We frame our discussion in the context of previous work from across a variety of disciplines, and conclude by outlining fundamental statistical challenges whose solutions will in turn serve to advance the science of network inference.