As the popularity of hierarchical point forecast reconciliation methods increases, there is a growing interest in probabilistic forecast reconciliation. Many studies have utilized machine learning or deep learning techniques to implement probabilistic forecasting reconciliation and have made notable progress. However, these methods treat the reconciliation step as a fixed and hard post-processing step, leading to a trade-off between accuracy and coherency. In this paper, we propose a new approach for probabilistic forecast reconciliation. Unlike existing approaches, our proposed approach fuses the prediction step and reconciliation step into a deep learning framework, making the reconciliation step more flexible and soft by introducing the Kullback-Leibler divergence regularization term into the loss function. The approach is evaluated using three hierarchical time series datasets, which shows the advantages of our approach over other probabilistic forecast reconciliation methods.

翻译：随着层次点预测协调方法的普及，概率预测协调日益受到关注。诸多研究运用机器学习或深度学习技术实现概率预测协调，并取得了显著进展。然而，这些方法将协调步骤视为固定且强制的后处理环节，导致精度与一致性之间存在折衷。本文提出一种新的概率预测协调方法。与现有方法不同，本文提出的方法将预测步骤与协调步骤融合至深度学习框架中，通过在损失函数中引入Kullback-Leibler散度正则化项，使协调步骤更具灵活性和软性。该方法基于三个层次时间序列数据集进行评估，结果显示本方法优于其他概率预测协调方法。