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Gaussian Process Regression Reviewed in the Context of Inverse Theory
Surveys in Geophysics ( IF 4.6 ) Pub Date : 2021-04-11 , DOI: 10.1007/s10712-021-09640-w
William Menke , Roger Creel

Abstract

We review Gaussian process regression (GPR) and analyze it in the context of Inverse Theory—the collection of techniques used in geophysics (among other fields) to understand the structure of data analysis problems and the quality of their solutions. By viewing GPR as a special case of generalized least squares (least squares with prior information), we derive expressions for a variety of standard Inverse Theory quantities, including the data and model resolution matrices, the importance (influence) vector, and the gradient of the solution with respect to a parameter. We study the impulse response in the one-dimensional continuum limit and provide formulas for its area and width. Finally, we demonstrate how the importance vector can be used to design an optimum GPR experiment, through a process we call importance winnowing.



中文翻译:

逆理论背景下的高斯过程回归

摘要

我们回顾了高斯过程回归(GPR),并在逆理论的背景下进行了分析。逆理论是地球物理领域(以及其他领域)使用的技术集合,旨在理解数据分析问题的结构及其解决方案的质量。通过将GPR视为广义最小二乘(具有先验信息的最小二乘)的特殊情况,我们得出了各种标准逆理论量的表达式,包括数据和模型分辨率矩阵,重要性(影响)向量以及梯度关于参数的解决方案。我们研究一维连续极限中的脉冲响应,并提供其面积和宽度的公式。最后,我们展示了重要性向量如何通过我们称为重要性风选的过程来设计最佳GPR实验。

更新日期:2021-04-11
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