Obtaining accurate probabilistic forecasts while respecting hierarchical information is an important operational challenge in many applications, perhaps most obviously in energy management, supply chain planning, and resource allocation. The basic challenge, especially for multivariate forecasting, is that forecasts are often required to be coherent with respect to the hierarchical structure. In this paper, we propose a new model which leverages a factor model structure to produce coherent forecasts by construction. This is a consequence of a simple (exchangeability) observation: permuting \textit{}base-level series in the hierarchy does not change their aggregates. Our model uses a convolutional neural network to produce parameters for the factors, their loadings and base-level distributions; it produces samples which can be differentiated with respect to the model's parameters; and it can therefore optimize for any sample-based loss function, including the Continuous Ranked Probability Score and quantile losses. We can choose arbitrary continuous distributions for the factor and the base-level distributions. We compare our method to two previous methods which can be optimized end-to-end, while enforcing coherent aggregation. Our model achieves significant improvements: between $11.8-41.4\%$ on three hierarchical forecasting datasets. We also analyze the influence of parameters in our model with respect to base-level distribution and number of factors.

翻译：在众多应用中，尤其在能源管理、供应链规划和资源分配等领域，获取精确的概率预测同时遵循层级信息是一项重要的操作挑战。基本挑战，尤其是针对多变量预测而言，在于预测结果需与层级结构保持一致性。本文提出了一种新模型，该模型利用因子模型结构，通过构造方式直接生成一致的预测。这一成果源于一个简单的（可交换性）观察：对层级中的基础层级序列进行置换不会改变其聚合结果。我们的模型采用卷积神经网络生成因子、因子载荷以及基础层级分布的参数；该模型能生成相对于其参数可微的样本；因此，它可以针对任何基于样本的损失函数进行优化，包括连续排序概率评分和分位数损失。我们可为因子和基础层级分布选择任意连续分布。我们将所提方法与两种先前已实现端到端优化并强制保持一致聚合的方法进行了比较。我们的模型在三个层级预测数据集上取得了显著改进：提升幅度达 $11.8-41.4\%$。我们还分析了模型中基础层级分布和因子数量等参数的影响。