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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 Chao en_US dc.contributor.author (Authors) 林家立 zh_TW dc.contributor.author (Authors) Lin, Chia Li en_US dc.creator (作者) 林家立 zh_TW dc.creator (作者) Lin, Chia Li en_US dc.date (日期) 2016 en_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) G0103354001 en_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) 103354001 zh_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/#G0103354001 en_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 experiment en_US dc.subject (關鍵詞) uniform design en_US dc.subject (關鍵詞) response surface methodology en_US dc.subject (關鍵詞) classification en_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 Approach en_US dc.type (資料類型) thesis en_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
