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

Kim, ByeongJip

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

Description

Title

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

Author(s)

Kim, ByeongJip

Issue Date

2025-06-30

Director of Research (if dissertation) or Advisor (if thesis)

Chen, Yuguo

Doctoral Committee Chair(s)

Chen, Yuguo

Committee Member(s)

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

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• 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

Abstract

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.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2025 ByeongJip Kim

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