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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 盧信銘(Hsin-Min Lu) | |
| dc.contributor.author | Ching-Ning Chen | en |
| dc.contributor.author | 陳靖甯 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:29:29Z | - |
| dc.date.available | 2016-08-24 | |
| dc.date.copyright | 2016-08-24 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-05 | |
| dc.identifier.citation | [1] Bishop, C.M., Pattern Recognition and Machine Learning (Information Science and Statistics). 2006: Springer-Verlag New York, Inc.
[2] Chang, C.-C. and C.-J. Lin, LIBSVM: A library for support vector machines. ACM Trans. Intell. Syst. Technol., 2011. 2(3): p. 1-27. [3] Coppersmith, D. and S. Winograd, Matrix multiplication via arithmetic progressions. J. Symb. Comput., 1990. 9(3): p. 251-280. [4] Eddelbuettel, D. and R. Francois, Rcpp: Seamless R and C++ Integration. Journal of Statistical Software, 2011. 40(8): p. 1-18. [5] Eddelbuettel, D. and C. Sanderson, RcppArmadillo: Accelerating R with high-performance C++ linear algebra. Computational Statistics and Data Analysis, 2014. 71: p. 1054-1063. [6] Farebrother, R.W., Linear least squares computations. 1988: Marcel Dekker, Inc. [7] Hartigan, J.A. and M.A. Wong, Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics), 1979. 28(1): p. 100-108. [8] IEEE Computer Society, IEEE Standard for Floating-Point Arithmetic. IEEE Std 754-2008, 2008: p. 1-70. [9] Krige, D.g., A Statistical Approach to Some Mine Valuation and Allied Problems on the Witwatersrand. 1951. [10] Meyer, D., et al., e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien. 2015. [11] Minka, T.P., A family of algorithms for approximate bayesian inference. 2001, Massachusetts Institute of Technology. p. 1. [12] Mises, R.V., Mathematical theory of probability and statistics. 1964: Academic Press. [13] Mohri, M., A. Rostamizadeh, and A. Talwalkar, Foundations of Machine Learning. 2012: The MIT Press. 480. [14] Neal, R.M., Regression and classification using Gaussian process priors. Bayesian statistics, 1998. 6: p. 475. [15] Nguyen-Tuong, D., J.R. Peters, and M. Seeger. Local Gaussian process regression for real time online model learning. in Advances in Neural Information Processing Systems. 2009. [16] R Core Team, R: A Language and Environment for Statistical Computing. 2016: Vienna, Austria. [17] Rasmussen, C.E., Gaussian Processes in Machine Learning, in Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures, O. Bousquet, U. von Luxburg, and G. Rätsch, Editors. 2004, Springer Berlin Heidelberg: Berlin, Heidelberg. p. 63-71. [18] Rasmussen, C.E. The SARCOS data. Data [cited 2016 7/20]; Available from: http://www.gaussianprocess.org/gpml/data/. [19] Rasmussen, C.E. and C.K.I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). 2005: The MIT Press. [20] Robinson, S., Toward an optimal algorithm for matrix multiplication. SIAM news, 2005. 38(9): p. 1-3. [21] Seeger, M., C. Williams, and N. Lawrence. Fast forward selection to speed up sparse Gaussian process regression. in Artificial Intelligence and Statistics 9. 2003. [22] Silverman, B.W., Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting. Journal of the Royal Statistical Society. Series B (Methodological), 1985. 47(1): p. 1-52. [23] Snelson, E. and Z. Ghahramani. Sparse Gaussian processes using pseudo-inputs. in Advances in neural information processing systems. 2005. [24] Wahba, G., Spline models for observational data. Vol. 59. 1990: Siam. [25] Wikipedia contributors. Machine learning. 12 July 2016 13:45 UTC 14 July 2016 15:59 UTC]; Available from: https://en.wikipedia.org/w/index.php?title=Machine_learning&oldid=729480417. [26] Wikipedia contributors. Sparse approximation. 13 July 2016 03:27 UTC 23 July 2016 05:59 UTC]; Available from: https://en.wikipedia.org/w/index.php?title=Sparse_approximation&oldid=729570141. [27] Wikipedia contributors. Supervised learning. 20 May 2016 09:35 UTC 12 July 2016 17:38 UTC]; Available from: https://en.wikipedia.org/w/index.php?title=Supervised_learning&oldid=721203892. [28] Williams, C.K.I. and D. Barber, Bayesian Classification With Gaussian Processes. IEEE Trans. Pattern Anal. Mach. Intell., 1998. 20(12): p. 1342-1351. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50090 | - |
| dc.description.abstract | 高斯程序迴歸（Gaussian Process Regression）為機器學習中的監督式學習方法之一。該方法具有良好的預測能力，但時間複雜度高，其訓練模型時必須算一行列數會隨著訓練資料集線性上升的反矩陣，因此當資料量大時，高斯程序訓練時間會過長。本篇論文提出一個以分群演算法來加速高斯程序訓練時間的方法，且實驗顯示在訓練資料集有四萬筆資料時能提升七十倍以上的訓練速度，並且僅降低極小程度的預測能力，勝過其他具代表性的加速方法。 | zh_TW |
| dc.description.abstract | Gaussian process (GP) regression are non-parametric supervised learning methods in the field of machine learning. GP methods has excellent prediction performance, but need too much time on training models, because it has to solve a square matrix whose number of rows and columns are linear to the number of training data points, resulting in cubed time complexity. We proposed a method that uses clustering algorithm to speed up the training phase and approximate the prediction. The experiments show that our method costs less than one seventieth time of original GP given the training set has forty thousand data points while the error does not grow much. Compared to other approximation methods, our method uses less time and obtain prediction of less error. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:29:29Z (GMT). No. of bitstreams: 1 ntu-105-R03725025-1.pdf: 1537744 bytes, checksum: ae852f442f54dda13b479f1b8c82f114 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS iv LIST OF FIGURES vi LIST OF TABLES vii Chapter 1 Introduction 1 Chapter 2 Literature Review 6 2.1 Gaussian Process 6 2.2 Gaussian Process Regression 9 2.3 Gaussian Process Classification 13 2.4 Approximation Methods 15 2.4.1 Subset of Regressors 15 2.4.2 Local Gaussian Process (LGP) 16 Chapter 3 Local Gaussian Process with K-means 19 3.1 An observation 19 3.2 How to Partition the Data Set? 21 3.3 Training and Prediction 24 3.4 Lower Limit of Training Time Complexity 26 Chapter 4 Experiments 28 4.1 SARCOS 28 4.2 Kin-40k 30 4.3 Pumadyn-32nm 32 4.4 How Number of Clusters Affect Prediction? 33 4.5 Closest Local Model Alone: Best Local Model? 37 4.6 Parameter Tuning with LGPK 38 Chapter 5 Conclusion and Future Work 40 REFERENCE 41 | |
| dc.language.iso | en | |
| dc.subject | 時間複雜度 | zh_TW |
| dc.subject | 分群 | zh_TW |
| dc.subject | 高斯程序 | zh_TW |
| dc.subject | 迴歸 | zh_TW |
| dc.subject | 監督式學習 | zh_TW |
| dc.subject | Supervised Learning | en |
| dc.subject | Time Complexity | en |
| dc.subject | Clustering | en |
| dc.subject | Gaussian Process | en |
| dc.subject | Regression | en |
| dc.title | 以分群演算法加速高斯程序迴歸 | zh_TW |
| dc.title | Scaling Gaussian Process Regression for Big Data | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 魏志平(Chih-Ping Wei),王釧茹(Chuan-Ju Wang) | |
| dc.subject.keyword | 分群,高斯程序,迴歸,監督式學習,時間複雜度, | zh_TW |
| dc.subject.keyword | Clustering,Gaussian Process,Regression,Supervised Learning,Time Complexity, | en |
| dc.relation.page | 42 | |
| dc.identifier.doi | 10.6342/NTU201602011 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-08-05 | |
| dc.contributor.author-college | 管理學院 | zh_TW |
| dc.contributor.author-dept | 資訊管理學研究所 | zh_TW |
| 顯示於系所單位： | 資訊管理學系 | |
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