Three Essays in Advanced Graph Neural Networks: From Multivariate Temporal Forecasting to Heterophilous Graph Learning

Abstract

In recent decades, the rapid advancement of computing power and data collection techniques has led to an unprecedented surge in structured and semi-structured data, necessitating the development of deep learning techniques to extract meaningful insights. While traditional deep learning methods have demonstrated remarkable power across various domains, they struggle to model the complex inter-relational structures inherent in real-world data, such as graphs. Graph Neural Networks (GNNs) have emerged as a powerful framework to address this limitation, enabling the effective representation of interdependent entities and achieving success in numerous real-world applications.

However, several challenges remain for GNNs, particularly in areas such as multivariate time series forecasting and heterophilous graph learning. For instance, while GNNs have been widely applied to multivariate time series forecasting, their potential in probabilistic forecasting remains under-explored. Most existing GNN-based forecasting models focus on deterministic predictions, failing to quantify predictive uncertainty, which is crucial for decision-making. Developing a GNN-based framework that effectively integrates probabilistic modelling into temporal forecasting remains an open challenge.

Additionally, GNNs are often incorporated into time series models to capture inter-series dependencies, while intra-series temporal dependencies are typically modelled separately using temporal models. However, in real-world systems, intra- and inter-temporal dependencies are inherently intertwined, making it challenging to fully exploit complex entangled relationships using existing methods. This raises the question of whether time series data can be transformed into a pure graph representation to unify these dependencies under a pure graph paradigm...