Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.

翻译：基于图的深度学习方法已成为处理相关时间序列集合的流行工具。与传统多变量预测方法不同，基于神经图的预测器通过利用成对关系，将预测条件建立在（可能动态的）跨越时间序列集合的图上。这种条件化可以表现为神经预测架构上的架构性归纳偏置，从而形成一类称为时空图神经网络的深度学习模型。这类关系性归纳偏置使得在大型时间序列集合上训练全局预测模型成为可能，同时通过考虑集合中元素（即图节点）之间的局部相关性（即图边），实现对集合中每个元素的预测局部化。事实上，图神经网络和深度学习在时间序列预测方面的最新理论和实践进展，使得采用此类处理框架既具有吸引力又恰逢其时。然而，文献中的大多数研究侧重于利用现代深度学习实践提出现有神经架构的变体，而基础性和方法论方面的问题尚未得到系统性研究。为填补这一空白，本文旨在引入一个全面的方法论框架，该框架形式化了预测问题，提供了基于图的预测模型的设计原则以及评估其性能的方法。同时，在概述该领域的基础上，我们提供了设计指南、建议和最佳实践，并对开放挑战和未来研究方向进行了深入讨论。