Collaborative Research: Towards a Theoretic Foundation for Optimal Deep Graph Learning

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Graph learning has become the cornerstone in numerous real-world applications, such as social media mining, brain connectivity analysis, computational epidemiology and financial fraud detection. Graph neural networks (GNNs for short) represent an important and emerging family of deep graph learning models. By producing a vector representation of graph elements, GNNs have largely streamlined a multitude of graph learning problems. In the vast majority of the existing works, they require a given graph, including its topology, the associated attribute information and labels for (semi-)supervised learning tasks, as part of the input of the corresponding learning model. Despite tremendous progress being made, a theoretical foundation of optimal deep graph learning is still missing, a gap that this project aims to fulfill. The outcomes of this project have broader impacts on education and society. The results of this project enrich the curriculum as well as summer outreach programs at participating institutions, and are further disseminated to the community through a variety of formats to create synergies and advance understandings of different disciplines. This project benefits a variety of high-impact graph learning based applications, including recommendation, power grid, neural science, team science and management, and intelligent transportation systems. This project examines the fundamental role of the input data, including graph topology, attributes and optional labels, in graph neural networks. There are three research thrusts in this project. The first thrust seeks to understand how sensitive the GNNs model is with respect to the input graph; how to quantify the uncertainty of the GNNs model; and how that impacts the generalization performance of the GNNs model. The second thrust develops algorithms to optimize the initially provided graph so as to maximally boost the generalization performance of the given GNNs model. The third thrust develops active learning methods based on deep reinforcement learning with entropy regularization to optimally obtain the additional labels to further improve the GNNs model. This project investigates new theoretic foundations in terms of the sensitivity, the uncertainty and the generalization performance of graph neural networks. It develops new algorithms for learning optimal graphs and active GNNs with better efficacy whose fundamental limits, including sample complexity, generalization error bound, optimality and convergence rate, are well understood. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.