Predictions in the form of probability distributions are crucial for
decision-making. Quantile regression enables this within spatial interpolation
settings for merging remote sensing and gauge precipitation data. However,
ensemble learning of quantile regression algorithms remains unexplored in this
context. Here, we address this gap by introducing nine quantile-based ensemble
learners and applying them to large precipitation datasets. We employed a novel
feature engineering strategy, reducing predictors to distance-weighted
satellite precipitation at relevant locations, combined with location
elevation. Our ensemble learners include six stacking and three simple methods
(mean, median, best combiner), combining six individual algorithms: quantile
regression (QR), quantile regression forests (QRF), generalized random forests
(GRF), gradient boosting machines (GBM), light gradient boosting machines
(LightGBM), and quantile regression neural networks (QRNN). These algorithms
serve as both base learners and combiners within different stacking methods. We
evaluated performance against QR using quantile scoring functions in a large
dataset comprising 15 years of monthly gauge-measured and satellite
precipitation in contiguous US (CONUS). Stacking with QR and QRNN yielded the
best results across quantile levels of interest (0.025, 0.050, 0.075, 0.100,
0.200, 0.300, 0.400, 0.500, 0.600, 0.700, 0.800, 0.900, 0.925, 0.950, 0.975),
surpassing the reference method by 3.91% to 8.95%. This demonstrates the
potential of stacking to improve probabilistic predictions in spatial
interpolation and beyond.

在空间插值和其他领域中，通过使用九种基于分位数的集成学习方法，将距离加权卫星降水数据与位置高程相结合，通过对比量化打分函数，证明了堆叠方法在提高概率预测方面的潜力。

卫星降水的空间插值中的不确定性估计与集成学习

Uncertainty estimation in spatial interpolation of satellite  precipitation with ensemble learning

To form precipitation datasets that are accurate and, at the same time, have
high spatial densities, data from satellites and gauges are often merged in the
literature. However, uncertainty estimates for the data acquired in this manner
are scarcely provided, although the importance of uncertainty quantification in
predictive modelling is widely recognized. Furthermore, the benefits that
machine learning can bring to the task of providing such estimates have not
been broadly realized and properly explored through benchmark experiments. The
present study aims at filling in this specific gap by conducting the first
benchmark tests on the topic. On a large dataset that comprises 15-year-long
monthly data spanning across the contiguous United States, we extensively
compared six learners that are, by their construction, appropriate for
predictive uncertainty quantification. These are the quantile regression (QR),
quantile regression forests (QRF), generalized random forests (GRF), gradient
boosting machines (GBM), light gradient boosting machines (LightGBM) and
quantile regression neural networks (QRNN). The comparison referred to the
competence of the learners in issuing predictive quantiles at nine levels that
facilitate a good approximation of the entire predictive probability
distribution, and was primarily based on the quantile and continuous ranked
probability skill scores. Three types of predictor variables (i.e., satellite
precipitation variables, distances between a point of interest and satellite
grid points, and elevation at a point of interest) were used in the comparison
and were additionally compared with each other. This additional comparison was
based on the explainable machine learning concept of feature importance. The
results suggest that the order from the best to the worst of the learners for
the task investigated is the following: LightGBM, QRF, GRF, GBM, QRNN and QR...

通过对具有 15 年长期月度跨越美国的大型数据集进行广泛比较，本研究旨在首次进行基于机器学习的不确定性量化任务的基准测试，结论表明适用于此任务的学习器的能力排名分别为：LightGBM，QRF，GRF，GBM，QRNN 和 QR。