Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation
Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation
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DOI：
10.1007/s11222-021-10014-w
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发表时间：
2018-07
影响因子：
2.2
通讯作者：
Xiong Lyu;M. Binois;M. Ludkovski
中科院分区：
文献类型：
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作者：
Xiong Lyu;M. Binois;M. Ludkovski
我们考虑了噪声黑盒函数超过给定阈值的水平集的学习问题。为了有效地重建水平集，我们研究了高斯过程(GP)元模型。我们的重点是强随机模拟器，特别是具有重尾模拟噪声和低信噪比的模拟器。为了防止噪声误指定，我们评估了三种变量的性能：(I)学生观察的GP；(Ii)学生过程(TPS)；以及(Iii)对反应符号建模的分类GP。结合这些元模型，我们分析了几种用于指导序贯实验设计的获取函数，将现有的逐步不确定性约简准则扩展到随机轮廓寻找环境中。这也促使我们开发(近似)更新公式来有效地计算这样的获取函数。我们的方案是通过使用1-6维的各种合成实验进行基准测试的。我们还考虑了水平集估计在确定百慕大期权在金融中的最优行使策略方面的应用。
We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-tobservations; (ii) Student-tprocesses (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.