# Hierarchically Regularized Deep Forecasting

arXiv: https://arxiv.org/abs/2106.07630 · HTML: https://mlsanity.com/paper/2106.07630/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Scaling Graph Neural Networks with Approximate PageRank](https://mlsanity.com/paper/2007.01570/) (2020)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [A Self-supervised Approach to Hierarchical Forecasting with Applications to Groupwise Synthetic Controls](https://mlsanity.com/paper/1906.10586/) (2019)
- [Hierarchical Dynamic Modeling for Individualized Bayesian Forecasting](https://mlsanity.com/paper/2101.03408/) (2021)

## Built on by (most cited first, 9 of 9)

- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures](https://mlsanity.com/paper/2110.13179/) (2021)
- [HierarchicalForecast: A Reference Framework for Hierarchical Forecasting in Python](https://mlsanity.com/paper/2207.03517/) (2022)
- [Scalable Probabilistic Forecasting in Retail with Gradient Boosted Trees: A Practitioner's Approach](https://mlsanity.com/paper/2311.00993/) (2023)
- [Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting](https://mlsanity.com/paper/2204.10414/) (2022)
- [Hierarchical Proxy Modeling for Improved HPO in Time Series Forecasting](https://mlsanity.com/paper/2211.15092/) (2022)
- [DeepHGNN: Study of Graph Neural Network based Forecasting Methods for Hierarchically Related Multivariate Time Series](https://mlsanity.com/paper/2405.18693/) (2024)
- [Hierarchically Coherent Multivariate Mixture Networks](https://mlsanity.com/paper/2305.07089/) (2023)

## Abstract (arXiv)

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy. The main challenge is to exploit the hierarchical correlations to simultaneously obtain good prediction accuracy for time series at different levels of the hierarchy. In this paper, we propose a new approach for hierarchical forecasting which consists of two components. First, decomposing the time series along a global set of basis time series and modeling hierarchical constraints using the coefficients of the basis decomposition. And second, using a linear autoregressive model with coefficients that vary with time. Unlike past methods, our approach is scalable (inference for a specific time series only needs access to its own history) while also modeling the hierarchical structure via (approximate) coherence constraints among the time series forecasts. We experiment on several public datasets and demonstrate significantly improved overall performance on forecasts at different levels of the hierarchy, compared to existing state-of-the-art hierarchical models.