Adaptive design for Gaussian process regression under censoring
Adaptive design for Gaussian process regression under censoring
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DOI：
10.1214/21-aoas1512
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发表时间：
2019-10
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影响因子：
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通讯作者：
Jialei Chen;Simon Mak;V. R. Joseph;Chuck Zhang
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文献类型：
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作者：
Jialei Chen;Simon Mak;V. R. Joseph;Chuck Zhang
工程问题的一个关键目标是在输入域上预测未知的实验曲面。在复杂的物理实验中，这可能会受到响应审查的阻碍，从而导致信息的重大损失。对于这样的问题，实验设计对于使用少量昂贵的实验运行来最大化预测能力至关重要。为了解决这个问题，我们提出了一种新的自适应设计方法，称为综合截除均方误差（ICMSE）方法。我们的ICMSE方法首先学习潜在的审查行为，然后自适应地选择在审查下预测不确定性最小的设计点。在具有积高斯相关函数的高斯过程回归模型下，所提出的ICMSE准则具有良好的封闭表达式，可实现高效的设计优化。我们在手术计划和晶圆制造两个实际应用中证明了ICMSE设计的有效性。
A key objective in engineering problems is to predict an unknown experimental surface over an input domain. In complex physical experiments, this may be hampered by response censoring, which results in a significant loss of information. For such problems, experimental design is paramount for maximizing predictive power using a small number of expensive experimental runs. To tackle this, we propose a novel adaptive design method, called the integrated censored mean-squared error (ICMSE) method. Our ICMSE method first learns the underlying censoring behavior, then adaptively chooses design points which minimize predictive uncertainty under censoring. Under a Gaussian process regression model with product Gaussian correlation function, the proposed ICMSE criterion has a nice closed-form expression, which allows for efficient design optimization. We demonstrate the effectiveness of the ICMSE design in the two real-world applications on surgical planning and wafer manufacturing.