End-to-end probabilistic hierarchical forecasting of large hierarchies via probabilistic top-down
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通过概率自上而下方法实现大型层级的端到端概率预测
- 研究问题
- 面对数十万条层级或分组需求序列，如何以可承受计算成本生成各层相互一致、保留跨序列依赖的概率预测？
- 方法与思路
- 作者只预测少量聚合序列，估计历史分解比例的联合分布，再通过概率自上而下抽样生成底层样本并加总到各层。
- 材料陈述的贡献
- 摘要称该方法在两个零售数据集的所列比较中取得最低加权尺度分位损失，并报告可在普通笔记本上完成大规模计算。
- 阅读关注点
- 应核对分解比例的联合建模、零需求与时变比例处理、训练测试划分，以及比较方法的调参与计算条件是否一致。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收未经核实；摘要中的性能与速度属于特定实验，不能推出其他层级数据上的普遍优势。
原文摘要
Retail and supply chain operations rely on demand forecasts to drive decisions, from replenishment at the product level to capacity planning at the store level. These forecasts should be probabilistic, to allow risk-aware decisions, and coherent across the aggregation hierarchy, so that decisions taken at different levels are not based on conflicting demand forecasts. Producing such forecasts is computationally demanding; at retail scale, with hierarchies of hundreds of thousands of time series, this cost becomes a primary concern. Existing two-step forecast-then-reconcile procedures and end-to-end neural models scale poorly, rely on restrictive assumptions, or require specialized hardware and engineering effort. We propose e2eTD, a scalable method for coherent probabilistic forecasting of large hierarchical and grouped time series. e2eTD directly forecasts only a small subset of aggregate series (about 0.3\% of the hierarchy in our experiments), which are smoother and thus more predictable than the intermittent bottom series. The resulting forecast samples are propagated to the bottom level through a novel probabilistic top-down sampling algorithm, in which the historical disaggregation proportions are modeled as joint distributions, estimated in-sample. Since the bottom samples retain the cross-series dependence, summing them yields coherent forecasts for all aggregation levels. On the M5 and Favorita datasets, e2eTD achieves the lowest weighted scaled pinball loss across aggregation levels among all competing methods; it would have ranked 11th of 892 teams in the M5 Uncertainty competition. On a standard laptop, e2eTD runs in about five minutes on M5 ($\sim$40K series) and twenty minutes on Favorita ($\sim$300K series).