Obtaining accurate probabilistic forecasts is an important operational challenge in many applications, perhaps most obviously in energy management, climate forecasting, supply chain planning, and resource allocation. In many of these applications, there is a natural hierarchical structure over the forecasted quantities; and forecasting systems that adhere to this hierarchical structure are said to be coherent. Furthermore, operational planning benefits from accuracy at all levels of the aggregation hierarchy. Building accurate and coherent forecasting systems, however, is challenging: classic multivariate time series tools and neural network methods are still being adapted for this purpose. In this paper, we augment an MQForecaster neural network architecture with a novel deep Gaussian factor forecasting model that achieves coherence by construction, yielding a method we call the Deep Coherent Factor Model Neural Network (DeepCoFactor) model. DeepCoFactor generates samples that can be differentiated with respect to model parameters, allowing optimization on various sample-based learning objectives that align with the forecasting system's goals, including quantile loss and the scaled Continuous Ranked Probability Score (CRPS). In a comparison to state-of-the-art coherent forecasting methods, DeepCoFactor achieves significant improvements in scaled CRPS forecast accuracy, with gains between 4.16 and 54.40%, as measured on three publicly available hierarchical forecasting datasets.

翻译：获取精确的概率预测是许多应用中的重要操作挑战，在能源管理、气候预测、供应链规划和资源分配等领域尤为明显。在这些应用中，预测量通常存在自然的层次结构；遵循这种层次结构的预测系统被称为具有一致性。此外，操作规划需要聚合层次所有层级上的预测准确性。然而，构建准确且一致的预测系统具有挑战性：传统的多元时间序列工具和神经网络方法仍在为此目的进行适配。本文中，我们通过一种新颖的深度高斯因子预测模型增强了MQForecaster神经网络架构，该模型通过构造实现一致性，形成我们称为深度一致性因子模型神经网络（DeepCoFactor）的方法。DeepCoFactor生成的样本可对模型参数进行微分，从而支持基于各种样本学习目标的优化，包括分位数损失和缩放连续分级概率评分（CRPS）。在与最先进的一致性预测方法比较中，DeepCoFactor在三个公开可用的层次预测数据集上实现了缩放CRPS预测准确性的显著提升，改进幅度介于4.16%至54.40%之间。