Existing 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：现有时间序列间的关联关系可被利用作为归纳偏置，以构建有效的预测模型。在分层时间序列中，子序列集合间的关联关系对预测值施加了硬约束（分层归纳偏置）。本文提出一种基于图的方法，在时间序列预测的深度学习背景下统一关系型与分层型归纳偏置。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层级结构的一个层次。通过利用现代可训练的图池化算子，我们证明即使层次结构先验未知，也可直接从数据中学习得到，从而获得与预测目标对齐的聚类分配。处理架构中嵌入可微分的协调阶段，使分层约束既作为架构偏置又作为预测的正则化元素。在代表性数据集上的仿真结果表明，所提方法相较于现有技术具有竞争力。