Statistical inference in complex networks: community detection, change-point detection, link prediction, and two-sample testing

Network data are non-Euclidean relational data that consist of vertices (nodes) and edges (links). Such relational data are ubiquitous in everyday life, appearing in systems like public transportation networks, social relationships on platforms such as social networking services, and user-generated reviews on websites like Yelp. Beyond these familiar examples, networks also span a wide range of domains\textemdash from macroscopic systems like the World Wide Web to microscopic ones like gene interactions. In the era of the Fourth Industrial Revolution and big data, the statistical analysis on network data has the power to intellectually inspire other related disciplines, as well as the statistical society. The cutting-edge data storage and acquisition in this era enable us to access massive network datasets from various academic domains. Given the wide variety of networks in the world, diverse theories and methods are required to study their unique characteristics. For example, networks can exhibit different types of nodes, e.g., both human nodes and product nodes in review networks like Yelp. In addition to heterogeneous node types, we often observe different link types frequently; for example, yeast networks can exhibit multiple link (interaction) types among genes. Networks can also evolve over time. For instance, online dynamic networks involve streaming datasets where graph snapshots arrive sequentially in real time, while offline dynamic networks capture historical data through a series of graph snapshots that are fully available at the time of analysis. The vast and varied landscape of network types, combined with the growing availability of complex network data, requires the development of novel theories and methodologies tailored to each context. However, traditional methods and theories are often not directly applicable to these new network data or leave spaces for significant improvement. This dissertation aims to extend existing theories and methods to more complex networks. Moreover, this dissertation develops new theories and methods for key statistical challenges in dynamic networks, including discovering the latent network structure (communities), detecting the structural changes (change points in dynamic networks), predicting the future networks when there is no change point in dynamic networks, and comparing different networks. The first three problems focus on a single network, which may be a uni-layer, multi-layer, or dynamic network. In contrast, the fourth problem focuses on the joint analysis of two multi-layer networks.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Kim, ByeongJip

Contributors dc:contributor

• Chen, Yuguo
• Agterberg, Joshua
• Dayanikli, Gokce
• Simpson, Douglas G.

• Statistical Network Analysis
• Latent Space Model
• Nonparametric Statistics
• Two-sample Testing
• Graphon
• Statistical Hypothesis Testing
• Dynamic Network
• Change Point Analysis
• Stochastic Block Model
• Variational Principle
• Multi-layer Network

Statement dc:rights

• Copyright 2025 ByeongJip Kim

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130133

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130133