Graph-based inference and learning with applications in finance

Thesis

Graph machine learning has emerged as a powerful tool for modelling intricate interconnections between data entities. These methods have been applied to diverse domains, from social science to molecular biology, offering unprecedented insights. However, a significant challenge is the need for an explicit and accurate graph as input, which is not always possible to obtain. This has led to the development of the discipline of Graph Learning, which focuses on inferring graph topologies from data observed on nodes of the graph.

Modern graph learning faces some challenges, such as incomplete datasets or complex topological properties that are difficult to incorporate into model specifications. To address these challenges, this thesis investigates model-based graph learning from various perspectives and proposes two novel methodologies: Kernel Graph Learning (KGL) and Learning to Learn Graph Topologies (L2G). KGL is developed from a functional perspective, offering a robust model that can handle noisy and missing node data by jointly inferring graphs and data distribution that affected by the graphs. L2G, on the other hand, employs a deep learning architecture to transform optimisation of graph adjacency matrices into a parametric functional mapping task, ensuring faster inference and precision in learning graphs with certain topological properties.

In terms of the practical implications, we focus on Quantitative Finance, where markets, institutions and assets are deeply interconnected. Although contemporary finance studies use graph representation to visualise the economic ties, the potential of graph machine learning and its ability to enhance forecasting is rarely explored. Learning a financial graph from a rich source of data also lacks exploration. This thesis aims to bridge this gap. By learning financial networks of assets from pricing data, we improve portfolio construction with better profitability. Additionally, a customised graph neural network model, GNNHAR, is developed to examine the non-linear volatility spillover effect in equity graphs and improve realised volatility forecasting.

Authors: Pu, X

• DOI: 10.5287/ora-kqmbgdpm6
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: realised volatility forecasting; deep learning; graph machine learning; portfolio construction; financial networks
• Subjects: Finance; Machine learning; Deep learning (Machine learning)