Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation
| Title: | Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation |
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| Authors: | Lyu, Xiong, Binois, Mickael, Ludkovski, Michael |
| Publication Year: | 2018 |
| Collection: | Computer Science Statistics |
| Subject Terms: | Statistics - Machine Learning, Computer Science - Machine Learning |
| More Details: | 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 samplers, 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-$t$ observations; (ii) Student-$t$ processes (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. Comment: 8 figures. Major update compared to v1 including multiple new sections and new plots. All Tables have been re-done |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1807.06712 |
| Accession Number: | edsarx.1807.06712 |
| Database: | arXiv |
| Description not available. |