Open Collections

Zhang, Congsong

University of British Columbia

Graph optimization problems (GOPs) are fundamental in both graph theory and artificial intelligence (AI), playing an important role in various real-world applications and motivating researchers to develop approaches to address them. With advancements in machine learning (ML), particularly deep learning, numerous approaches using ML techniques, such as graph neural networks (GNNs), have been developed for GOPs. These methods focus on learning graph representations to approximate solutions, with some directly interpreting these representations as vertex probabilities to generate solutions. However, these learned representations often lack the incorporation of domain-specific human expertise that adheres to the properties of GOPs, reducing interpretability and limiting their effectiveness to generating approximate solutions rather than exact ones. In this thesis, we present an interpretable graph distribution representation learning that integrates domain-specific knowledge adhering to specific GOPs. Additionally, we implement this novel learning with GNN models. The proposed distribution representation consists of two basic components: marginal distributions and copula parameters. Marginal distributions capture the likelihood of potential solution values for GOPs, while copula parameters model the dependencies among these values, ensuring their adherence to the problem's constraints. Building on these learned representations, we propose a heuristic to search for exact solutions of GOPs by extracting rich solution information embedded within the learned distributions. This heuristic computes the Shannon entropy for each search path, prioritizing those with the least uncertainty. By generalizing the search process at a high level, the heuristic becomes broadly applicable to diverse problems while keeping its effectiveness for specific problems through the integration of domain-specific knowledge. In addition, we explore the connection between intersection graph models and GNN models. We prove a phase transition in the diameters of two random intersection graph models, offering valuable insights into the underlying properties of GNN models.

Text

2025-07-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/91523

Computer Science

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/