Data Reduction for Subsample in Gaussian Process

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：112

、訪客IP：3.138.125.86

姓名

陳志剛(Chih-Kang Chen) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Data Reduction for Subsample in Gaussian Process)

相關論文

★ Optimal Multi-platform Designs Based on Two Statistical Approaches	★ Subdata Selection : A- and I-optimalities
★ On the Construction of Multi-Stratum Factorial Designs	★ A Compression-Based Partitioning Estimate Classifier
★ On the Study of Feedforward Neural Networks: an Experimental Design Approach	★ Bayesian Optimization for Hyperparameter Tuning with Robust Parameter Design
★ Unreplicated Designs for Random Noise Exploration	★ Optimal Designs for Simple Directed/Weighted Network Structures
★ Study on the Prediction Capability of Two Aliasing Indices for Gaussian Random Fields	★ Predictive Subdata Selection for Gaussian Process Modeling
★ Optimal Designs on Undirected Network Structures for Network-Based Models	★ Gaussian Process Modeling with Weighted Additive Kernels

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2026-6-30以後開放)

摘要(中)

高斯隨機過程模型為一在電腦實驗廣泛使用的模型，其具備良好的預測能力。然
而，配適此模型會牽涉到反矩陣的運算，因此當資料量龐大時相當耗時。近年來科技
的發展導致資料的取得更為便利，卻也同時加劇了資料縮減的需求。本論文的研究目
的便是透過資料縮減的方式，來減少高斯隨機過程模型配適造成的運算成本。本文提
出的方法會在維持模型參數特性的情況下，進行資料縮減並同時提升模型的預測能力。
此外在進行資料縮減的過程中，此方法不需要預先指定縮減的資料量，而是在縮減的
過程中利用數據的特性找出最適當的資料量。本文以許多模擬實例來展示此方法之優
點。最後，透過高斯模型跟多維常態分佈的關聯，本文所提出的方法與 Mallow’s Cp 有
相似之處。本文亦闡述我們的方法與 Mallow’s Cp 之相似之處並比較。

摘要(英)

Gaussian processes (GPs) are commonly used for emulating large-scale computer experiments. However, parameter estimation is computationally intensive for a GP model
given massive data because it involves the computation of the inverse of a big correlation matrix. Recently, thanks to technological evolution, collecting data is getting easier.
However, a great mass of data incurs the requirement for data reduction. Our purpose is
to lessen the computational burden through data reduction. Our method maintains the
characteristics of model parameters and improves the performance of predictions. Besides,
instead of giving a size of reduced data in advance, we also try to find a proper size of
the reduced data. We conduct several simulations for illustration. Additionally, from the
connection between the GP and the multivariate normal distribution, we find that our
method has an aspect in common with the Mallow’s Cp, a model selection criterion for
linear regression. We also compare our method with the Mallow’s Cp.

關鍵字(中)

★ 高斯過程
★ 資料縮減
★ 數據選取
★ Mallow’s Cp

關鍵字(英)

★ Gaussian process
★ Data reduction
★ Data selection
★ Mallow’s Cp

論文目次

Chinese Abstract i
Abstract ii
Contents iii
List of Figures iv
List of Tables v
1 Introduction 1
2 Literature Review and Preliminaries 2
2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Gaussian Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Mallow’s Cp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Methodology 8
3.1 Bootstraped the Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Greedy Search by Minimizing Mean-Squared Prediction Error . . . . . . . 8
3.3 Modification of Mallow’s Cp . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Simulation 11
4.1 Currin et al. (1998) Exponential Function . . . . . . . . . . . . . . . . . . 12
4.2 Borehole Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.3 Wing Weight Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4 Welch et al. (1992) Function . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.5 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.6 Cp Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Real Data Analysis 20
6 Conclusion 22
References 23

參考文獻

Ababou, R., Bagtzoglou, A. C., and Wood, E. F. (1994). “On the Condition
Number of Covariance Matrices in Kriging, Estimation, and Simula-tion of Random
Fields,＂Mathematical Geology, 26, 99–133.
Cheng, Q., Wang, H. Y., Yang, M. (2020). “Information-based optimal subdata
selection for big data logistic regression,＂J. Stat. Plan Inference. 2020, 209, 112–122.
Chu, T., Zhu, J. and Wang, H. (2011).“Penalized Maximum Likelihood Estimation
and Variable Selection in Geostatistics,＂The Annals of Statistics, 39, 2607-2625.
Cressie, N. (1993). “Statistics for Spatial Data (2nd ed.),＂New York: Wiley,
Cressie, N., and Johannesson, G. (2008).“Fixed Rank Kriging for Very Large Data
Sets,＂J. R. Stat. Soc. Series B, 70, 209-226.
Davis, G. J. and Morris, M. D. (1997). “Six Factors Which Affect the Condition
Number of Matrices Associated With Kriging,＂Mathematical Geology, 29, 669-683.
Diamond, P., and Armstrong, M. (1984). “Robustness of Variograms and Conditioning of Kriging Matrices,＂Mathematical Geology, 16, 809-822.
Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife,＂The Annals
of Statistics, 71, 1-26.
Floater, M. S., and Iske, A. (1996).“Multistep Scattered Data Interpolation Using
Compactly Supported Radial Basis Functions,＂J. Comput. Appl. Math., 73, 65-78.
MR1424869.
Gramacy, R. B. and Apley, D. W. (2015).“Local Gaussian Process Approximation
for Large Computer Experiments,＂J. Comput. Graph. Stat., 24, 561-578.
Gramacy, R. B., and Polson, N. (2011). “Particle Learning of Gaussian Process
Models for Sequential Design and Optimization,＂J. Comput. Graph. Stat., 20, 102-118.
Haaland, B., and Qian, P. (2011). “Annals Accurate Emulators for Large-scale
Computer Experiments,＂The Annals of Statistics, 39, 2974-3002.
Hoeting, J., Madigan, D., Raftery, A., and Volinsky, C. (1999). “Bayesian
Model Averaging: A Tutorial,＂Statistical Science, 14, 382-417.
Hoeting, J., Davis, R., Merton, A. and Thompson, S. (2006). “Model Selection
for Geostatistical Models,＂Ecological Applications, 16, 87-98.
Huang, H. and Chen, C. (2007). “Optimal Geostatistical Model Selection,＂Journal
of the American Statistical Association, 102, 1009-1024.
Joseph, V., Hung, Y. and Sudjianto, A. (2008). “Blind Kriging: A New Method
for Developing Metamodels,＂Journal of Mechanical Design, 130, 031102.
Joseph, V. and Vakayil, A. (2021).“SPlit: An Optimal Method for Data Splitting,＂
Stewart School of Industrial and Systems Engineering Georgia Institute of Technology,
Atlanta, GA 30332, USA,
Kaufman, C. G., Bingham, D., Habib, S., Heitmann, K. and Frieman, J. A.
(2011). “Efficient Emulators of Computer Experiments Using Compactly Supported
Correlation Functions, with an Application to Cosmology,＂The Annals of Applied
Statistics, 5, 2470-2492.
Linkletter, C., Bingham, D., Hengartner, N., Higdon, D. and Ye, K. Q.
(2006). “Variable selection for Gaussian process models in computer experiments,＂
Technometrics, 48, 478-490.
Mallows, C. L.(1973). “Some Comments on Cp,＂Technometrics., 15, 661–675.
Patterson, H.D. and Thompson, R. (2014). “Recovery of Inter-Block Information
When Block Size Are Unequal,＂Biometrika., 58, 545-554.
Peng, C. Y. and Wu, C. F. J. (2014).“On the Choice of Nugget in Kriging Modeling
for Deterministic Computer Experiment,＂J. Comput. Graph. Stat., 23, 151-168.
Posa D. (1989).“Conditioning of the Stationary Kriging Matrices for Some Well-Known
Covariance Models,＂Mathematical Geology, 21, 755-765.
Pronzato, L. and Rendas, M. J. (2017). “Bayesian Local Kriging,＂Technometrics
2017, 59, 293-304.
Salagame, R. R. and Barton, R. R. (1997). “Factorial Hypercube Designs for
Spatial Correlation Regression,＂J. Appl. Stat., 24, 453-473.
Snelson, E. and Ghahramani, Z. (2006).“Sparse Gaussian Processes Using PseudoInputs,＂Advances in Neural Information Processing Systems, Cambridge, MA: MIT
Press, pp. 1257–1264.
Sung, C. L., Gramacy, R.B. and Haaland1, B. (2018). “Exploiting Variance
Reduction Potential in Local Gaussian Process Search,＂Statistical Science, 28, 577-
600.
Sung, C. L., Wang, W., Plumlee, M. and Haaland, B. (2020). “Multiresolution
Functional ANOVA for Large-scale, Many-input Computer Experiments,＂Journal of
the American Statistical Association, 115, 908-919.
Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T. J. and
Morris, M. D. (1992). “Screening, Predicting, and Computer Experiments,＂Technometrics, 34, 15-25.
Zou, H. and Li, R. (2008). “One-step Sparse Estimates in Nonconcave Penalized
Likelihood Models,＂The Annals of Statistics, 36, 1509-1533.
Yibo Zhao, Yasuo Amemiya and Ying Hung(2018). “Efficirnt Gaussian Process
Modeling Using Experimental Design-based Subagging,＂Statistical Science, 28, 1459-
1479.

指導教授

張明中(Ming-Chung Chang)

審核日期

2021-7-26

推文