A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is relatively high given limited data points. Gaussian process models with additive correlation functions are scalable to dimensionality, but they are more restrictive as they only work for additive functions. In this work, we consider a projection pursuit model, in which the nonparametric part is driven by an additive Gaussian process regression. We choose the dimension of the additive function higher than the original input dimension, and call this strategy "dimension expansion". We show that dimension expansion can help approximate more complex functions. A gradient descent algorithm is proposed for model training based on the maximum likelihood estimation. Simulation studies show that the proposed method outperforms the traditional Gaussian process models. The Supplementary Materials are available online.
翻译:计算机实验的一个主要目标是通过分散的评估来重建计算机代码赋予的功能。传统的异热带高斯过程模型在由于数据点有限而投入层面相对较高的情况下会受到维度的诅咒。高斯过程模型具有累加相关功能,可以伸缩到维度,但由于它们只用于添加功能,因此更具限制性。在这项工作中,我们考虑一个投影追踪模型,其中非对称部分由添加的高斯进程回归驱动。我们选择了比原始输入层面更高的添加功能维度,并将这一战略称为“二元扩展 ” 。我们表明,尺寸扩展可以帮助大约地达到更复杂的功能。根据最大可能性估计,为模型培训建议了一个梯度下移算法。模拟研究表明,拟议的方法优于传统的高斯进程模型。补充材料可在网上查阅。