Abstract

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.

中文翻译：

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基于聚类的Kriging近似算法，降低了复杂度

摘要

克里格或高斯过程回归作为非线性回归模型以及替代模型在进化计算领域中的广泛应用。但是，克里格的计算和空间复杂度（分别在数据点数量上为三次方和二次方）成为当今越来越多的可用数据的主要瓶颈。在本文中，我们提出了一种用于降低复杂性的通用方法，称为聚类Kriging，该方法将整个数据集划分为较小的聚类，并在其之上构建多个Kriging模型。另外，在新框架内，提出了四种克里格近似算法作为候选算法。这些算法中的每一个都可以应用于更大的数据集，同时保持Kriging的优势和强大功能。在定义良好的测试框架上，对所提出的算法进行了详细说明，并与大量现有的最先进的克里格近似方法进行了经验比较。根据经验研究，提出的算法始终优于现有算法。此外，为使用提出的算法提供了一些实用的建议。