Graph Deep Learning for Time Series Forecasting

Abstract:
Neural networks have been used to forecast time series for decades. One of the key elements enabling most of the field's recent achievements is the training of a single neural network on large collections of related time series. This approach, however, often considers each time series independently from the others and, consequently, discards dependencies that might be instrumental for accurate predictions. Nonetheless, the alternative of modeling the full collection as a large multivariate time series cannot scale as it does not exploit the structure of the data to reduce computational and sample complexity. In this research, we aim to address the shortcomings of the state of the art in correlated time series forecasting by relying on graph representations and graph deep learning methods. We propose graph-based predictors that model pairwise relationships among time series by conditioning forecasts on a (possibly dynamic) graph spanning the collection. The conditioning is implemented as an architectural bias directly embedded into the processing; as we will show, this inductive bias enables the training of global forecasting models on large sensor networks by accounting for local correlations (graph edges) among time series (graph nodes). Our research introduces a comprehensive methodological framework characterizing the family of these predictive models and provides design principles for graph-based forecasting. Within this context, we propose methods to tackle the inherent challenges of the field, i.e., dealing with missing data, sparse observations, local effects, and latent relational dependencies. The computational scalability of the proposed framework is also addressed, together with methodologies enabling transfer learning and hierarchical forecasting. Extensive empirical results validate the introduced methodologies and place graph deep learning methods among the most important tools available in modern forecasting.

Dissertation Committee:
- Prof. Cesare Alippi, Università della Svizzera italiana, Switzerland (Research Advisor)
- Prof. Michael Bronstein, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Luca Maria Gambardella, Università della Svizzera italiana, Switzerland (Internal Member)
- Prof. Davide Bacciu, Università di Pisa, Italy (External Member)
- Prof. Mathias Niepert, University of Stuttgart, Germany (External Member)
- Prof. Peter Tino, University of Birmingham, UK (External Member)