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：用于超时时时时间序列分析的图形神经网络的杰出成就表明,关系限制在神经预报结构中引入了有效的感化偏差。然而,通常缺乏作为基本数据生成过程特征的关联信息,执业者面临从相关图表数据中推论随后处理阶段使用相关图表的数据的问题。我们提出了新的、原则性――但实际的基于概率的计分方法,这些方法既能了解在分布图上的关系依赖性,又能控制所学图表的宽度和可计算性。拟议的图表学习框架以基于蒙特卡洛分得分梯度估算的综合差异减少技术为基础,以理论为基础,而且如我们所显示的那样,在实践中是有效的。在本文件中,我们侧重于时间序列预测问题,并表明,通过根据图形学习问题调整梯度估测度,我们能够达到最新水平的业绩,同时控制所学图表的宽度和可计算性。我们实证地评估了拟议方法在合成和真实世界评分梯度基准上的综合差异减少技术的实效,显示,并且正如我们所显示的那样,在实际中,我们注重的时间序列预测问题,显示,通过将拟议的预测程序,可将拟议的方法用作一个直径方的图表的图形的模型的校正分析程序。