There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there has been growing interest in the machine learning community for such methods, primarily driven by the success of deep Gaussian process regression approaches and deep convolutional neural networks. These methods are often computationally expensive to train and implement and consequently, there has been a resurgence of interest in random projections and deep learning models based on random weights -- so called reservoir computing methods. Here, we combine several of these ideas to develop the Random Ensemble Deep Spatial (REDS) approach to predict spatial data. The procedure uses random Fourier features as inputs to an extreme learning machine (a deep neural model with random weights), and with calibrated ensembles of outputs from this model based on different random weights, it provides a simple uncertainty quantification. The REDS method is demonstrated on simulated data and on a classic large satellite data set.

翻译：最近人们对为非常庞大的数据集和(或)预测领域开发空间预测算法的兴趣很大,这些方法主要是在空间统计界开发的,但对于这类方法的机器学习界的兴趣日益浓厚,这主要是由深高山进程回归法和深层进化神经网络的成功推动的。这些方法往往计算成本昂贵,用于培训和实施,因此,人们重新对随机的预测和基于随机重量的深层学习模型 -- -- 即所谓的储油层计算方法 -- -- 感兴趣。在这里,我们结合了其中的若干想法,以开发随机综合深层空间(REDS)预测空间数据的方法。该程序使用随机的Fourier特征作为极端学习机器(一种带有随机重量的深线性模型)的投入,并使用根据不同随机重量校准的模型产出组合,提供了简单的不确定性量化。REDS方法在模拟数据和经典大型卫星数据集上演示。