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題名 以機器學習方法估計電腦實驗之目標區域
Estimation of Target Regions in Computer Experiments: A Machine Learning Approach
作者 林家立
Lin, Chia Li
貢獻者 洪英超
Hung, Ying Chao
林家立
Lin, Chia Li
關鍵詞 電腦實驗
均勻設計
反應曲面法
分類模型
computer experiment
uniform design
response surface methodology
classification
日期 2016
上傳時間 2-Aug-2016 15:53:14 (UTC+8)
摘要 電腦實驗(computer experiment)是探索複雜系統輸出反應值和輸入參數之間關係的重要工具，其重要特性是每一次的實驗非常耗費時間及運算的成本。一般在電腦實驗中，研究者較常關心的多是反應曲面的配適和輸出反應值的最佳化等問題(如極大或極小值)。借由一真實平行分散處理系統的啟發，本文所關心的是如何找出系統反應值的局部目標區域。此目標區域有一個非常重要的特性，即區域內外的輸出值所呈現的反應曲面並不連續，因此一般傳統的反應曲面法(response surface methodology)無法適用。本文提出一個新的、可估計不同類型電腦實驗目標區域的有效方法，其中包含了逐步均勻設計和建立分類模型的概
念，電腦模擬的結果也證明了所提方法準確又有效率。
Computer experiment has been an important tool for exploring the relationships between the input factors and the output responses. It’s important feature is that conducting an experiment is usually time consuming and computationally expensive. In general, researchers are more interested in finding an adequate model for the response surface and the related output optimization problems over the entire input space. Motivated by a real-life parallel and distributed system, here we focus on finding a localized “target region” for the computer experiment. The experiment here has an important characteristic - the response surface is not continuous over the target region of interest. Thus, the traditional response surface methodology (RSM) cannot be directly applied. In this thesis, a novel and efficient methodology for estimating this type of target regions of computer experiment is proposed. The method incorporates the concept of sequential uniform design (UD) and the development of classification techniques based on support vector machines (SVM). Computer simulation shows that the proposed method can efficiently and precisely estimate the target region of
computer experiment with different shapes.
參考文獻 Box, G.E.P., Drapper, D.R., (1987), “Empirical Model Building and Response Surfaces,”
John Wiley & Sons, New York.
Chen, R.B., Hsu, Y.W., Hung, Y., Wang, W. (2012), “Central Composite Discrepany-
Based Uniform Designs for Irregular Experimental Regions,” Computational Statistics & Data Analysis.
Cheng, C.S., Li, K.C., (1995), “A study of the method of principal Hessian direction
for analysis of data from design experiments,” Statistica Sinica 5, 617-639.
Chuang, S.C., Hung, Y.C. (2010), “Uniform design over general input domains with
applications to target region estimation in computer experiments,” Computational Statistics & Data Analysis, 54, 219-232.
Fang, K.T., Lin, D.J., Winker, P., and Zhang, Y. (2000), “Uniform Design: Theory and
Applications,“ Technometrics, 42, 237-248.
Hickernell, F.J., (1999), “Goodness-of-fit statistics, discrepancies and robust designs,”
Statistics & Probability Letters 44, 73-78.
Huang, C.M., Lee, Y.J., Lin, D.K.J., Huang, S.Y., (2007), “Model selection for support vector machines via uniform design,” Computational Statistics & Data Analysis 52,
335-346.
Hung, Y.C., Chang, C.C., (2008), “Dynamic scheduling for switched processing systems with substantial service-mode switching times,” Queneing Systems: Theory
and Applications 60, 87-109.
Johnson, M.E., Moore, L.M., and Ylvisaker, D. (1990), “Minimax and Maximin
Distance Designs,” Journal of Statistical Planning and Inference. 26. 131-148.
Keerthi, S.S., Lin, C.J., (2003), “Asymptotic behaviors of support vector machines
with Gaussian kernel,” Neural Computation 15, 1667-1689.
McKay, M.D., Beckman, R.J., and Conover, W.J. (1979), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a
Computer Code,” Technometrics, 21, 239-245.
Owen, A.B. (1992), “Orthogonal Arrays for Computer Experiments, Integration and
Visualization,” Statistica Sinica, 2, 439-452.
Ranjan, P., Bingham, D., and Michailidis, G. (2008), “Sequential Experimental Design for Contour Estimation From Complex Computer Codes,” Technometrics, 50, 527-
541.
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P., (1989). “Design and Analysis of
Computer Experiments,” Statistical Science, 4, 409-423.
Tang, B. (1993), “Orthogonal Array-Based Latin Hypercubes,” Journal of the American
Statistical Association, 88, 1392-1397.
Vapnik, V.N., (1998), “Statistical Learning Theory,” Wiley, New York.
Wang, D., Zhang, X., Fan, M. and Ye, X., (2015), “An Efficient Classifier Based on Hierarchical Mixing Linear Support Vector Machines,” IJCAI, AAAI Press, 3897-
3903.
Wu, C.F.J., Hamada, M., (2000), “Experiments: Planning, Analysis, and Parameter
Design,” Wiley, New York
描述 碩士
國立政治大學
統計學系
103354001
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354001
資料類型 thesis
dc.contributor.advisor 洪英超zh_TW
dc.contributor.advisor Hung, Ying Chaoen_US
dc.contributor.author (Authors) 林家立zh_TW
dc.contributor.author (Authors) Lin, Chia Lien_US
dc.creator (作者) 林家立zh_TW
dc.creator (作者) Lin, Chia Lien_US
dc.date (日期) 2016en_US
dc.date.accessioned 2-Aug-2016 15:53:14 (UTC+8)-
dc.date.available 2-Aug-2016 15:53:14 (UTC+8)-
dc.date.issued (上傳時間) 2-Aug-2016 15:53:14 (UTC+8)-
dc.identifier (Other Identifiers) G0103354001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99530-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 103354001zh_TW
dc.description.abstract (摘要) 電腦實驗(computer experiment)是探索複雜系統輸出反應值和輸入參數之間關係的重要工具，其重要特性是每一次的實驗非常耗費時間及運算的成本。一般在電腦實驗中，研究者較常關心的多是反應曲面的配適和輸出反應值的最佳化等問題(如極大或極小值)。借由一真實平行分散處理系統的啟發，本文所關心的是如何找出系統反應值的局部目標區域。此目標區域有一個非常重要的特性，即區域內外的輸出值所呈現的反應曲面並不連續，因此一般傳統的反應曲面法(response surface methodology)無法適用。本文提出一個新的、可估計不同類型電腦實驗目標區域的有效方法，其中包含了逐步均勻設計和建立分類模型的概
念，電腦模擬的結果也證明了所提方法準確又有效率。		zh_TW
dc.description.abstract (摘要) Computer experiment has been an important tool for exploring the relationships between the input factors and the output responses. It’s important feature is that conducting an experiment is usually time consuming and computationally expensive. In general, researchers are more interested in finding an adequate model for the response surface and the related output optimization problems over the entire input space. Motivated by a real-life parallel and distributed system, here we focus on finding a localized “target region” for the computer experiment. The experiment here has an important characteristic - the response surface is not continuous over the target region of interest. Thus, the traditional response surface methodology (RSM) cannot be directly applied. In this thesis, a novel and efficient methodology for estimating this type of target regions of computer experiment is proposed. The method incorporates the concept of sequential uniform design (UD) and the development of classification techniques based on support vector machines (SVM). Computer simulation shows that the proposed method can efficiently and precisely estimate the target region of
computer experiment with different shapes.		en_US
dc.description.tableofcontents 第一章 緒論 1
第二章 問題與研究方法 3
第一節 電腦實驗之目標區域偵測 3
第二節 均勻設計 6
第三節 目標區域之分類模型建構 8
第三章 電腦模擬 17
第一節 分段線性邊界之目標區域 17
第二節 非線性邊界之目標區域 21
第四章 結論與探討 27
第五章 參考文獻 28		zh_TW
dc.format.extent 1295496 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354001en_US
dc.subject (關鍵詞) 電腦實驗zh_TW
dc.subject (關鍵詞) 均勻設計zh_TW
dc.subject (關鍵詞) 反應曲面法zh_TW
dc.subject (關鍵詞) 分類模型zh_TW
dc.subject (關鍵詞) computer experimenten_US
dc.subject (關鍵詞) uniform designen_US
dc.subject (關鍵詞) response surface methodologyen_US
dc.subject (關鍵詞) classificationen_US
dc.title (題名) 以機器學習方法估計電腦實驗之目標區域zh_TW
dc.title (題名) Estimation of Target Regions in Computer Experiments: A Machine Learning Approachen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Box, G.E.P., Drapper, D.R., (1987), “Empirical Model Building and Response Surfaces,”
John Wiley & Sons, New York.
Chen, R.B., Hsu, Y.W., Hung, Y., Wang, W. (2012), “Central Composite Discrepany-
Based Uniform Designs for Irregular Experimental Regions,” Computational Statistics & Data Analysis.
Cheng, C.S., Li, K.C., (1995), “A study of the method of principal Hessian direction
for analysis of data from design experiments,” Statistica Sinica 5, 617-639.
Chuang, S.C., Hung, Y.C. (2010), “Uniform design over general input domains with
applications to target region estimation in computer experiments,” Computational Statistics & Data Analysis, 54, 219-232.
Fang, K.T., Lin, D.J., Winker, P., and Zhang, Y. (2000), “Uniform Design: Theory and
Applications,“ Technometrics, 42, 237-248.
Hickernell, F.J., (1999), “Goodness-of-fit statistics, discrepancies and robust designs,”
Statistics & Probability Letters 44, 73-78.
Huang, C.M., Lee, Y.J., Lin, D.K.J., Huang, S.Y., (2007), “Model selection for support vector machines via uniform design,” Computational Statistics & Data Analysis 52,
335-346.
Hung, Y.C., Chang, C.C., (2008), “Dynamic scheduling for switched processing systems with substantial service-mode switching times,” Queneing Systems: Theory
and Applications 60, 87-109.
Johnson, M.E., Moore, L.M., and Ylvisaker, D. (1990), “Minimax and Maximin
Distance Designs,” Journal of Statistical Planning and Inference. 26. 131-148.
Keerthi, S.S., Lin, C.J., (2003), “Asymptotic behaviors of support vector machines
with Gaussian kernel,” Neural Computation 15, 1667-1689.
McKay, M.D., Beckman, R.J., and Conover, W.J. (1979), “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a
Computer Code,” Technometrics, 21, 239-245.
Owen, A.B. (1992), “Orthogonal Arrays for Computer Experiments, Integration and
Visualization,” Statistica Sinica, 2, 439-452.
Ranjan, P., Bingham, D., and Michailidis, G. (2008), “Sequential Experimental Design for Contour Estimation From Complex Computer Codes,” Technometrics, 50, 527-
541.
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P., (1989). “Design and Analysis of
Computer Experiments,” Statistical Science, 4, 409-423.
Tang, B. (1993), “Orthogonal Array-Based Latin Hypercubes,” Journal of the American
Statistical Association, 88, 1392-1397.
Vapnik, V.N., (1998), “Statistical Learning Theory,” Wiley, New York.
Wang, D., Zhang, X., Fan, M. and Ye, X., (2015), “An Efficient Classifier Based on Hierarchical Mixing Linear Support Vector Machines,” IJCAI, AAAI Press, 3897-
3903.
Wu, C.F.J., Hamada, M., (2000), “Experiments: Planning, Analysis, and Parameter
Design,” Wiley, New York		zh_TW