Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often, a few parameters are sufficient to parameterize the covariance function, and maximum likelihood (ML) methods can be used to estimate these parameters from data. ML methods, however, are computationally demanding. For example, in the case of local likelihood estimation, even fitting covariance models on modest size windows can overwhelm typical computational resources for data analysis. This limitation motivates the idea of using neural network (NN) methods to approximate ML estimates. We train NNs to take moderate size spatial fields or variograms as input and return the range and noise-to-signal covariance parameters. Once trained, the NNs provide estimates with a similar accuracy compared to ML estimation and at a speedup by a factor of 100 or more. Although we focus on a specific covariance estimation problem motivated by a climate science application, this work can be easily extended to other, more complex, spatial problems and provides a proof-of-concept for this use of machine learning in computational statistics.

中文翻译：

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使用神经网络快速估计空间高斯过程模型的协方差参数

高斯过程 (GP) 是一种流行的空间参考数据模型，允许进行描述性陈述、新位置的预测以及新领域的模拟。通常，几个参数就足以参数化协方差函数，并且可以使用最大似然 (ML) 方法从数据中估计这些参数。然而，ML 方法在计算上要求很高。例如，在局部似然估计的情况下，即使在中等大小的窗口上拟合协方差模型也会压倒典型的数据分析计算资源。这种限制激发了使用神经网络 (NN) 方法来近似 ML 估计的想法。我们训练神经网络以中等大小的空间场或变异函数作为输入，并返回范围和噪声信号协方差参数。一经训练，与 ML 估计相比，NN 提供的估计精度相似，并且速度提高了 100 倍或更多。尽管我们专注于由气候科学应用激发的特定协方差估计问题，但这项工作可以轻松扩展到其他更复杂的空间问题，并为机器学习在计算统计中的这种使用提供了概念验证。