Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements of up to 26% on most datasets compared to state-of-the-art baselines. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to the more traditional bottom-up modeling.

翻译：概率性层次一致预测是许多实际预测应用中的关键问题——其目标是针对按预定义树状层次结构排列的大量时间序列，获得一致的、概率性的预测结果。本文提出了一种端到端的深度概率模型用于层次预测，该模型受经典自顶向下策略启发。该模型联合学习根时间序列的分布，以及每个父时间序列在任意时刻分配给其子节点的（Dirichlet）比例。由此产生的预测自然具有一致性，并为层次结构中的所有时间序列提供概率预测。我们在多个公共数据集上进行实验，结果表明，与最先进的基线方法相比，我们在大多数数据集上取得了高达26%的显著改进。最后，我们还从理论上论证了自顶向下方法相较于更传统的自底向上建模的优势。