# Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting

arXiv: https://arxiv.org/abs/2204.10414 · HTML: https://mlsanity.com/paper/2204.10414/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [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)
- [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)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures](https://mlsanity.com/paper/2110.13179/) (2021)
- [Hierarchically Regularized Deep Forecasting](https://mlsanity.com/paper/2106.07630/) (2021)
- [On the benefits of maximum likelihood estimation for Regression and Forecasting](https://mlsanity.com/paper/2106.10370/) (2021)
- [A Self-supervised Approach to Hierarchical Forecasting with Applications to Groupwise Synthetic Controls](https://mlsanity.com/paper/1906.10586/) (2019)
- [Machine learning applications in time series hierarchical forecasting](https://mlsanity.com/paper/1912.00370/) (2019)

## Built on by (most cited first, 3 of 3)

- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Hierarchically Coherent Multivariate Mixture Networks](https://mlsanity.com/paper/2305.07089/) (2023)
- [Hierarchical Forecast Reconciliation on Networks: A Network Flow Optimization Formulation](https://mlsanity.com/paper/2505.03955/) (2025)

## Abstract (arXiv)

Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements of up to 26% on most datasets compared to state-of-the-art baselines. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to the more traditional bottom-up modeling.