# Hierarchical Forecasting at Scale

arXiv: https://arxiv.org/abs/2310.12809 · HTML: https://mlsanity.com/paper/2310.12809/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression](https://mlsanity.com/paper/2106.01682/) (2021)
- [Deep Learning based Forecasting: a case study from the online fashion industry](https://mlsanity.com/paper/2305.14406/) (2023)
- [Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings](https://mlsanity.com/paper/1410.4726/) (2014)
- [Point and probabilistic forecast reconciliation for general linearly constrained multiple time series](https://mlsanity.com/paper/2305.05330/) (2023)

## Built on by (most cited first, 4 of 4)

- [Value-oriented forecast reconciliation for renewables in electricity markets](https://mlsanity.com/paper/2501.16086/) (2025)
- [Hierarchical Time Series Forecasting Via Latent Mean Encoding](https://mlsanity.com/paper/2506.19633/) (2025)
- [Cascaded Transfer: Learning Many Tasks under Budget Constraints](https://mlsanity.com/paper/2601.21513/) (2026)
- [High-Frequency Pricing at Scale for E-Commerce](https://mlsanity.com/paper/2606.13741/) (2026)

## Abstract (arXiv)

Existing hierarchical forecasting techniques scale poorly when the number of time series increases. We propose to learn a coherent forecast for millions of time series with a single bottom-level forecast model by using a sparse loss function that directly optimizes the hierarchical product and/or temporal structure. The benefit of our sparse hierarchical loss function is that it provides practitioners a method of producing bottom-level forecasts that are coherent to any chosen cross-sectional or temporal hierarchy. In addition, removing the need for a post-processing step as required in traditional hierarchical forecasting techniques reduces the computational cost of the prediction phase in the forecasting pipeline. On the public M5 dataset, our sparse hierarchical loss function performs up to 10% (RMSE) better compared to the baseline loss function. We implement our sparse hierarchical loss function within an existing forecasting model at bol, a large European e-commerce platform, resulting in an improved forecasting performance of 2% at the product level. Finally, we found an increase in forecasting performance of about 5-10% when evaluating the forecasting performance across the cross-sectional hierarchies that we defined. These results demonstrate the usefulness of our sparse hierarchical loss applied to a production forecasting system at a major e-commerce platform.