Relationships among time series can be exploited as inductive biases in learning effective forecasting models. In hierarchical time series, relationships among subsets of sequences induce hard constraints (hierarchical inductive biases) on the predicted values. In this paper, we propose a graph-based methodology to unify relational and hierarchical inductive biases in the context of deep learning for time series forecasting. In particular, we model both types of relationships as dependencies in a pyramidal graph structure, with each pyramidal layer corresponding to a level of the hierarchy. By exploiting modern - trainable - graph pooling operators we show that the hierarchical structure, if not available as a prior, can be learned directly from data, thus obtaining cluster assignments aligned with the forecasting objective. A differentiable reconciliation stage is incorporated into the processing architecture, allowing hierarchical constraints to act both as an architectural bias as well as a regularization element for predictions. Simulation results on representative datasets show that the proposed method compares favorably against the state of the art.

翻译：时间序列之间的关系可作为归纳偏置用于学习有效的预测模型。在分层时间序列中，子序列间的关系会对预测值产生硬约束（分层归纳偏置）。本文提出一种基于图的方法论，旨在时间序列预测的深度学习框架中统一关系性与分层性归纳偏置。具体而言，我们将两类关系建模为金字塔图结构中的依赖关系，其中每个金字塔层对应一个层级。通过利用现代可训练图池化算子，我们证明若分层结构无法作为先验知识获取，可直接从数据中学习该结构，从而获得与预测目标对齐的聚类分配。处理架构中集成了可微调和阶段，使得分层约束既能作为架构偏置，也能作为预测的正则化要素。在典型数据集上的仿真结果表明，所提方法相较于现有技术具有优越性。