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研究生: 莊世鐘
Shih-Chung Chuang
論文名稱: 廣泛區域之均勻設計與電腦實驗之運用
Uniform Design over General Input Domains with Applications to Computer Experiments
指導教授: 樊采虹
Tsai-Hung Fan
洪英超
Ying-Chao Hung
口試委員:
學位類別: 博士
Doctor
系所名稱: 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度: 98
語文別: 英文
論文頁數: 40
中文關鍵詞: 目標區域電腦實驗均勻設計廣泛區域
外文關鍵詞: target detection, computer experiment, uniform design
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  • 近年來,均勻設計在電腦實驗上廣被應用。在傳統均勻設計的發展中,其重心為單位超立方體區域上之均勻佈點。然而,最近我們發現在許多電腦的模擬當中,會面臨需在非矩形區域上做均勻設計的問題。因此在本研究當中,我們改進傳統均勻設計的方法,使其適用在更廣泛的區域上做佈點設計。此外,本論文同時提供一套具高效率的演算法來降低均勻設計時所需耗費的時間,同時也會藉由實例來驗證此演算法的有效性。接著,在應用當中,我們亦提出一套目標區域估計的演算法,此演算法主要是利用逐步均勻設計加上適當的迴歸模型來提高對目標區域偵測的效率。文末,我們也會以一些實際的例子來評估以上演算法效用;在這些例子當中,我們固定電腦模擬可進行的次數,然後比較各種不同方法對目標區域偵測的結果,從中可以發現,本論文所提之演算法所得到的估計結果均優於其它現有方法。


    The power of uniform design (UD) has received great attention in the area of computer experiments over the last two decades. However, when conducting a typical computer experiment, one finds many non-rectangular types of input domains on which traditional UD methods can not be adequately applied. In this study, we propose a new UD method that is suitable for any types of design area. For practical implementation, we develop an efficient algorithm to construct a socalled nearly uniform design (NUD) and show that it approximates very well the UD solution for small sizes of experiment. By utilizing the proposed UD method, we also develop a methodology for estimating the target region of computer experiments. The methodology is sequential and aims to (i) provide adaptive models that predict well the output measures related to the experimental target; and (ii) minimize the number of experimental trials. Finally, we illustrate the developed methodology on various examples and show that, given the same experimental budget, it outperforms other approaches in estimating the prespecified target region of computer experiments.

    1 Introduction and Motivating Examples 1 2 Uniform Design over General Input Domains 6 2.1 Introduction to Uniform Design . . . . . . . . . . . . . . . . . . 6 2.2 A New Measure of Uniformity: Central Composite Discrepancy . 8 2.3 The Weighted Uniform Design . . . . . . . . . . . . . . . . . . . 10 2.4 Construction of Nearly Uniform Designs . . . . . . . . . . . . . . 11 2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3 Methodology for Target Region Estimation 17 3.1 Choosing the Weight Function f(x) for UD . . . . . . . . . . . . 18 3.2 Fitting Response Models . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Sequential Weighted Uniform Design for Target Region Estimation 22 4 Performance Assessment 25 5 Concluding Remarks 35 Bibliography 37

    [1] Andre, J., P. Siarry, T. Dognon. 2000. An improvement of the standard genetic algorithm fighting premature convergence. Advances in Engineering Software 32(1) 49-60.
    [2] Armony, M., N. Bambos. 2003. Queueing dynamics and maximal throughput scheduling in switched processing systems. Queueing Systems: Theory and Applications 44 209-252.
    [3] Boser, B.E., I.M. Guyon, V.N. Vapnik. 1992. A training algorithm for optimal margin classifiers. The 5th Annual ACM Workshop on COLT, 144-152.
    [4] Box, G.E.P., D.R. Drapper. 1987. Empirical Model Building and Response Surfaces. John Wiley & Sons, New York.
    [5] Cheng, C.S., K.C. Li. 1995. A study of the method of principal Hessian direction for analysis of data from design experiments. Statistica Sinica, 5 617-639.
    [6] Cortes, C., V.N. Vapnik. 1995. Support vector networks. Machine Learning 20 273-297.
    [7] Fang, K.T. 1980. The uniform design: application of number-theoretic methods in experimental design. Acta. Math. Appl. Sinica 3 363-372.
    [8] Fang, K.T., F.J. Hickernell. 1995. The uniform design and its applications. Bull. Inst. Internat. Statist., 50th Session, Book 1, 333-349.
    [9] Fang, K.T., D.K.J. Lin. 2003. Uniform experimental designs and their applications in industry. Handbook of Statistics 22 131-170.
    [10] Fang, K.T., D.K.J. Lin, P. Winker, Y. Zhang. 2000. Unifrom design: theory and applications. Technometrics 42 237-248.
    [11] Fang, K.T., C.X. Ma, P. Winker. 2001. Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform design. Mathematical Computation 71 275-296.
    [12] Fang, K.T., H. Qin. 2003. A note on construction of nearly uniform designs with large number of runs. Statistics and Probability Letters 61 215-224.
    [13] Fang, K.T., W.C. Shiu, J.X. Pan. 1999a. Uniform designs based on Latin squares. Statistica Sinica 9 905-912.
    [14] Fang, K.T., G.L. Tian, M.Y. Xie. 1999b. Uniform design over a convex polyhedron. Chinese Science Bulletin 44 112-114.
    [15] Fang, K.T., Y. Wang. 1994. Number-theoretic Methods in Statistics. Chapman and Hall, London.
    [16] Fang, Y. 1995. Relationships between uniform design and orthogonal design. The 3rd International Chinese Statistical Association Conference, Beijing.
    [17] Guyon, I.M., B.E. Boser, V.N. Vapnik. 1993. Automatic capacity tuning of very large VC-dimension classifiers. Adv. in Neural Inform. Processing Systems 5 147-155.
    [18] Henderson, C.R. 1975. Best Linear unbiased estimation and prediction under a selection model. Biometrics 31, 423-447.
    [19] Hickernell, F.J. 1998. A generalized discrepancy and quadrature error bound. Math. Comput. 67 299-322.
    [20] Hickernell, F.J. 1999. Goodness-of-fit statistics, discrepancies and robust dessigns. Statis. Probab. Lett. 44 73-78.
    [21] Hsu, C.W., C.C. Chang, C.J. Lin. 2003. A practical guide to support vector classification. Technical Report CWH03a, Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan.
    [22] Huang, C.M., Y.J. Lee, D.K.J. Lin, S.Y. Huang. 2007. Model selection for support vector machines via uniform design. Computational Statistics & Data Analysis 52 335-346.
    [23] Hung, Y.C., C.C. Chang. 2008. Dynamic scheduling for switched processing systems with substantial service-mode switching times. Queueing Systems: Theory and Applications 60 87-109.
    [24] Hung, Y.C., G. Michailidis. 2008. Modeling, scheduling, and simulation of switched processing systems. ACM Transactions on Modeling and Computer Simulation 18, Article 12.
    [25] Hung, Y.C., G. Michailidis, D.R. Bingham. 2003. Developing efficient simulation methodology for complex queueing networks. Proceedings of the Winter Simulation Conference, New Orleans. 152-159.
    [26] Jones, D., M. Schonlau, W. Welch. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13, 455-492.
    [27] Keerthi, S.S., C.-J. Lin. 2003. Asymptotic behaviors of support vector machines with Gaussian kernel. Neural Computation 15 1667-1689.
    [28] Ma, C.X. 1997a. A new criterion of uniformity - symmetrical discrepancy. J. Nankai University 30 30-37.
    [29] Ma, C.X. 1997b. Construction of uniform designs using symmetrical discrepancy. Application of Statistics and Manegement 166-169.
    [30] Ma, C.X., K.T. Fang. 2004. A new approach to construction of nearly uniform designs. International Journal of Materials and Product Technology 20 115-126.
    [31] Ranjan, R., D. Bingham, G. Michailidis. 2008. Sequential experiment design for contour estimation from complex computer codes. To appear in Technometrics.
    [32] Sacks, J., W.J.Welch, T.J. Mitchell, H.P.Wynn. (1989). Design and analysis of computer Experiments. Statistical Science 4 409-423.
    [33] Santner, T.J., B.J. Williams, W.I. Notz. 2003. Design and Analysis of Computer Experiments. Springer-Verlag, New York.
    [34] Sch¨olkopf, B. 1997. Support Vector Learning. R. Oldenbourg Verlag, Munich.
    [35] Sharma, S. 1996. Applied Multivariate Techniques. Wiley.
    [36] Vapnik, V.N. 1995. The Nature of Statistical Learning Theory. Springer, New York.
    [37] Vapnik, V.N. 1998. Statistical Learning Theory. Wiley, New York.
    [38] Wang, Y., Fang, K.T. 1981. A note on uniform distribution and experimental design. KeXue TongBao 26 485-489.
    [39] Winker, P., Fang, K.T., 1998. In: Niederreiter, H., Zinterhof, P., Hellekalek, P. (Eds.), Optimal U-type design. Monte Carlo and Quasi-Monte Carlo Methods 1996. Springer, 436-448.
    [40] Wu, C.F.J., M. Hamada. 2000. Experiments: Planning, Analysis, and Parameter Design. Wiley, New York.

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