Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.

翻译：图神经网络在时空时间序列分析中的卓越成就表明，关系约束为神经预测架构引入了有效的归纳偏置。然而，表征底层数据生成过程的关系信息往往不可用，实践者面临从数据推断应在后续处理阶段使用何种关系图的问题。我们提出新颖、有原则且实用的基于概率得分的方法，该方法将关系依赖关系学习为图上的分布，同时以端到端方式最大化任务性能。所提出的图学习框架基于用于蒙特卡洛得分梯度估计的成熟方差缩减技术，具有理论基础，并且如我们所示，在实践中有效。本文聚焦时间序列预测问题，并通过将梯度估计器定制为图学习问题，展示了在控制所学习图稀疏性和计算可扩展性的同时，实现最先进性能的能力。我们通过合成和真实世界基准数据实证评估了所提方法的有效性，表明该解决方案既可作为独立的图识别程序，也可作为端到端预测架构的图学习组件。