# M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond

arXiv: https://arxiv.org/abs/2107.06675 · HTML: https://mlsanity.com/paper/2107.06675/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 14 Jul 2021.

## Builds on (most cited first, 8 of 8)

- [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)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories](https://mlsanity.com/paper/2005.01365/) (2020)
- [deepregression: a Flexible Neural Network Framework for Semi-Structured Deep Distributional Regression](https://mlsanity.com/paper/2104.02705/) (2021)
- [XGBoostLSS -- An extension of XGBoost to probabilistic forecasting](https://mlsanity.com/paper/1907.03178/) (2019)
- [Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices](https://mlsanity.com/paper/2010.01844/) (2020)

## Built on by (most cited first, 11 of 11)

- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Probabilistic forecasting of German electricity imbalance prices](https://mlsanity.com/paper/2205.11439/) (2022)
- [Distributional Gradient Boosting Machines](https://mlsanity.com/paper/2204.00778/) (2022)
- [Foundation Models for Demand Forecasting via Dual-Strategy Ensembling](https://mlsanity.com/paper/2507.22053/) (2025)
- [Scalable Probabilistic Forecasting in Retail with Gradient Boosted Trees: A Practitioner's Approach](https://mlsanity.com/paper/2311.00993/) (2023)
- [Simulation-based Forecasting for Intraday Power Markets: Modelling Fundamental Drivers for Location, Shape and Scale of the Price Distribution](https://mlsanity.com/paper/2211.13002/) (2022)
- [Online Distributional Regression](https://mlsanity.com/paper/2407.08750/) (2024)
- [High-Resolution Peak Demand Estimation Using Generalized Additive Models and Deep Neural Networks](https://mlsanity.com/paper/2203.03342/) (2022)
- [Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2504.02518/) (2025)
- [Intermittent time series forecasting: local vs global models](https://mlsanity.com/paper/2601.14031/) (2026)
- [Distributional Adaptive Soft Regression Trees](https://mlsanity.com/paper/2210.10389/) (2022)

## Abstract (arXiv)

The M5 competition uncertainty track aims for probabilistic forecasting of sales of thousands of Walmart retail goods. We show that the M5 competition data faces strong overdispersion and sporadic demand, especially zero demand. We discuss resulting modeling issues concerning adequate probabilistic forecasting of such count data processes. Unfortunately, the majority of popular prediction methods used in the M5 competition (e.g. lightgbm and xgboost GBMs) fails to address the data characteristics due to the considered objective functions. The distributional forecasting provides a suitable modeling approach for to the overcome those problems. The GAMLSS framework allows flexible probabilistic forecasting using low dimensional distributions. We illustrate, how the GAMLSS approach can be applied for the M5 competition data by modeling the location and scale parameter of various distributions, e.g. the negative binomial distribution. Finally, we discuss software packages for distributional modeling and their drawback, like the R package gamlss with its package extensions, and (deep) distributional forecasting libraries such as TensorFlow Probability.