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。