Gaussian Process Modeling with Weighted Additive Kernels

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吳炳璋(Bing-Jhang Wu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Gaussian Process Modeling with Weighted Additive Kernels)

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至系統瀏覽論文 (2026-6-30以後開放)

摘要(中)

電腦實驗在如今變得愈來愈熱門，高斯隨機過程因為具備高靈活性及內插性質，而成為其中一種被廣泛用在電腦實驗的代理模型。此外，高斯隨機過程對於複雜的反應曲面也具有相當優秀的預測表現。一個常見用來定義高斯隨機過程的共變異數函數的方法就是使用相乘性核函數。然而，當有兩個資料點離得太遠時，相乘性核函數可能會表現不佳。為了克服此問題，我們提出一個新的加權相加性核函數，其將相乘性核函數視為特例。我們透過模擬結果和實際資料來展現這個新方法具有較好的預測和解釋能力。

摘要(英)

Computer experiments have become more and more popular nowadays. Gaussian processes (GPs) are one of the widely used surrogate models for computer simulators due to their high flexibility and the property of interpolation. GPs also possess good prediction performance for complex response surfaces. A common way for defining the covariance function of a GP is to use a product kernel. However, the product kernel may result in bad performance especially when two inputs have a large lower-dimensional distance. To circumvent this problem, we propose a new weighted additive kernel, which treats the product kernel as a special case. We show that the new kernel leads to better prediction and interpretation performance under several simulated examples and real datasets.

關鍵字(中)

★ 電腦實驗
★ 相加模型
★ 相關函數

關鍵字(英)

★ Kriging
★ Computer experiments
★ Additive models
★ Correlation function

論文目次

Chinese Abstract i
Abstract ii
Contents iii
List of Figures iv
1 Introduction 1
2 Literature Review 2
3 Methodology 4
4 Simulation 8
4.1 Estimating weights by MLE . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.2 Estimating weights by iteration algorithm . . . . . . . . . . . . . . . . . . 12
5 Real Data Analysis 14
6 Conclusion 16
References 17

參考文獻

Cressie. N. A. C. (1993). Statistics for Spatial Data. Revised edition: Wiley, New York, NY, 1993 (900 pp.).

Deng, X., Lin, C. D., Liu, K. W., and Rowe, R. K. (2017). Additive Gaussian process for computer models with qualitative and quantitative factors. Technometrics 59(3), 283-292.

Duvenaud, D. K., Nickisch, H., and Rasmussen, C. E. (2011). Additive Gaussian processes. Advances in Neural Information Processing Systems., 24, 226-234.

Lin, L. H. and Joseph, V. R. (2019). Transformation and Additivity in Gaussian Processes. Technometrics, to appear.

MacDonald, B., Ranjan, P., and Chipman, H. (2015). GPfit: An R package for fitting a Gaussian process model to deterministic simulator outputs. Journal of Statistical Software 64(12), 1-23.

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL = https://www.R-project.org/.

Vollert, N., Ortner, M., and Pilz, J. (2019). Robust additive Gaussian process models using reference priors and cut-off-designs. Appl. Math. Model. 65, 586-596.

指導教授

張明中(Ming-Chung Chang)

審核日期

2021-7-26

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