# Combinations of distributional regression algorithms with application in uncertainty estimation of corrected satellite precipitation products

arXiv: https://arxiv.org/abs/2407.01623 · HTML: https://mlsanity.com/paper/2407.01623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 74 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [Using stacking to average Bayesian predictive distributions](https://mlsanity.com/paper/1704.02030/) (2017)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Distributional Regression Forests for Probabilistic Precipitation Forecasting in Complex Terrain](https://mlsanity.com/paper/1804.02921/) (2018)
- [The Evolution of Boosting Algorithms - From Machine Learning to Statistical Modelling](https://mlsanity.com/paper/1403.1452/) (2014)
- [A review of machine learning concepts and methods for addressing challenges in probabilistic hydrological post-processing and forecasting](https://mlsanity.com/paper/2206.08998/) (2022)
- [Forecast Evaluation of Quantiles, Prediction Intervals, and other Set-Valued Functionals](https://mlsanity.com/paper/1910.07912/) (2019)
- [Comparison of machine learning algorithms for merging gridded satellite and earth-observed precipitation data](https://mlsanity.com/paper/2301.01252/) (2022)
- [Hydrological post-processing for predicting extreme quantiles](https://mlsanity.com/paper/2202.13166/) (2022)
- [Merging satellite and gauge-measured precipitation using LightGBM with an emphasis on extreme quantiles](https://mlsanity.com/paper/2302.03606/) (2023)
- [Ensemble learning for blending gridded satellite and gauge-measured precipitation data](https://mlsanity.com/paper/2307.06840/) (2023)
- [Ensemble learning for uncertainty estimation with application to the correction of satellite precipitation products](https://mlsanity.com/paper/2403.10567/) (2024)
- [Uncertainty estimation of machine learning spatial precipitation predictions from satellite data](https://mlsanity.com/paper/2311.07511/) (2023)

## Abstract (arXiv)

To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct advantages over quantile regression, including the ability to model intermittency as well as a stronger ability to extrapolate beyond the training data, which is critical for predicting extreme precipitation. Therefore, here, we introduce the concept of distributional regression in precipitation dataset creation, specifically for the spatial prediction task of correcting satellite precipitation products. Building upon this concept, we formulated new ensemble learning methods that can be valuable not only for spatial prediction but also for other prediction problems. These methods exploit conditional zero-adjusted probability distributions estimated with generalized additive models for location, scale and shape (GAMLSS), spline-based GAMLSS and distributional regression forests as well as their ensembles (stacking based on quantile regression and equal-weight averaging). To identify the most effective methods for our specific problem, we compared them to benchmarks using a large, multi-source precipitation dataset. Stacking was shown to be superior to individual methods at most quantile levels when evaluated with the quantile loss function. Moreover, while the relative ranking of the methods varied across different quantile levels, stacking methods, and to a lesser extent mean combiners, exhibited lower variance in their performance across different quantiles compared to individual methods that occasionally ranked extremely low. Overall, a task-specific combination of multiple distributional regression algorithms could yield significant benefits in terms of stability.