Distance-Distributed Design for Gaussian Process Surrogates
Distance-Distributed Design for Gaussian Process Surrogates
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DOI：
10.1080/00401706.2019.1677269
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发表时间：
2018-12
期刊：
影响因子：
2.5
通讯作者：
Boya Zhang;D. Cole;R. Gramacy
中科院分区：
文献类型：
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作者：
Boya Zhang;D. Cole;R. Gramacy
摘要 计算机实验及相关领域的一个常见挑战是利用少量样本有效地探索输入空间，即实验设计问题。最近计算机实验文献中的大部分焦点（通常通过高斯过程（GP）代理进行建模）都集中在通过最大最小距离、拉丁超立方体等进行空间填充设计。然而，很容易凭经验证明，当模型超参数化未知时，此类设计会令人失望，并且必须根据在所选设计站点观察到的数据进行估计。即使性能指标是基于预测的，或者感兴趣的目标本质上或最终是连续的，例如在黑盒（贝叶斯）优化中，情况也是如此。在这里，我们揭露了这种低效率，表明在许多情况下，纯粹的随机设计优于更高功率的替代方案。然后，我们通过对随机设计的质量进行逆向工程，提出了一系列新方案，这些方案给出了 GP 长度尺度的最佳估计。具体来说，我们研究设计元素之间的成对距离的分布，并开发一种数值方案来优化给定样本大小和维度的这些距离。我们说明了基于距离的设计及其与更传统的空间填充方案的混合如何在静态（一次性设计）和顺序设置中表现出色。
Abstract A common challenge in computer experiments and related fields is to efficiently explore the input space using a small number of samples, that is, the experimental design problem. Much of the recent focus in the computer experiment literature, where modeling is often via Gaussian process (GP) surrogates, has been on space-filling designs, via maximin distance, Latin hypercube, etc. However, it is easy to demonstrate empirically that such designs disappoint when the model hyperparameterization is unknown, and must be estimated from data observed at the chosen design sites. This is true even when the performance metric is prediction-based, or when the target of interest is inherently or eventually sequential in nature, such as in blackbox (Bayesian) optimization. Here we expose such inefficiencies, showing that in many cases a purely random design is superior to higher-powered alternatives. We then propose a family of new schemes by reverse engineering the qualities of the random designs which give the best estimates of GP length scales. Specifically, we study the distribution of pairwise distances between design elements, and develop a numerical scheme to optimize those distances for a given sample size and dimension. We illustrate how our distance-based designs, and their hybrids with more conventional space-filling schemes, outperform in both static (one-shot design) and sequential settings.