課程名稱 |
多變量統計分析 Multivariates Statistical Analysis |
開課學期 |
104-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
陳 宏 |
課號 |
MATH7610 |
課程識別碼 |
221 U6160 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
必修 |
上課時間 |
星期二8,9(15:30~17:20)星期四2(9:10~10:00) |
上課地點 |
天數302天數302 |
備註 |
總人數上限:40人 外系人數限制:10人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1042MATH7610_ |
課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. 資訊檢索: PageRank, Graphs, and Markov Chain (Multivariate Analysis and 4V)
2. 資本資產訂價模式(CAPM)in practice: Asset Allocation in investment (Mean-Variance Analysis, Markowitz portfolio theory): Multivariate Random Variables: Matrix Algebra, Random Vectors, Quadratic Forms, and Multinormal Distribution
3. Statistical Inferences for Multivariate Distributions
4. Dimensional Reduction: Principal component Analysis, Factor Analysis (reduce a large number of variables to smaller), and Random Projection
5. Default Probability (違約機率): Classification, Discriminant Analysis , Predicting group membership.
6. Cluster Analysis: Identify homogeneous subgroups of cases or variables based on some measure of distance.
7. Canonical Correlation Analysis |
課程目標 |
1. Learn basic techniques for analysis of multi-dimensional data and big data.
2. Study multivariate distributions, especially Gaussian distribution.
3. Understand multivariate statistical inference and applications such as
discriminant analysis and cluster analysis.
4. Discuss various methods for dimension reduction, including principal component
analysis, factor analysis, Canonical Correlation Analysis, etc. |
課程要求 |
Solid knowledge on calculus, probability and statistics.
Familiarity with linear algebra. |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Johnson, R.A. and Wichern, D.W. (2007) Applied Multivariate Statistical
Analysis. Pearson Prentice Hall. (textbook)
Haerdle, W. and Simar, L. (2007) Applied Multivariate Statistical Analysis [本校電子書]
Izenman, A. (2008) Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning [本校電子書]
Everitt, B. and Hothorn, T. (2011) An Introduction to Applied Multivariate Analysis with R [本校電子書]
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參考書目 |
Flury, B. (1997) A First Course In Multivariate Statistics. Springer.
Srivastava, M. S. (2002) Methods of Multivariate Statistics. Wiley
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Quiz |
10% |
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2. |
Final/Project |
30% |
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3. |
Midterm |
30% |
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4. |
Homework |
30% |
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週次 |
日期 |
單元主題 |
第1週 |
2/23, 2/25 |
Tuesday & Wednesday: 4V in Big Data, PageRank, Graph, and Social Network; Random projection on reduce amount of data |
第2週 |
3/01, 3/03 |
Tuesday: Talk about Random Projection. |
第3週 |
3/08, 3/10 |
Tuesday: population PCA, functional data
Thursday: Multivariate Normal distribution; Matrix Algebra and Random Vectors |
第4週 |
3/15, 3/17 |
Tuesday and Thursday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN
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第5週 |
3/22, 3/24 |
Tuesday: Derive MLE and finish up Chapter 4.3-4.6
Thursday: Finish Chapter 4.
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第6週 |
3/29, 3/31 |
Tuesday: Chapter 5.1-5.6; Thursday: Finish Chapter 5 and EM algorithm.
Pagerank (reference: http://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf
http://www.cems.uvm.edu/~tlakoba/AppliedUGMath/other_Google/Wills.pdf)
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第7週 |
4/07 |
factor analysis |
第8週 |
4/12, 4/14 |
Tuesday: EM algorithm
Thursday: Class is cancelled.
Please refer to http://episte.math.ntu.edu.tw/entries/en_lagrange_mul/index.html on idea of Lagrange multiplier
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第9週 |
4/19, 4/21 |
Tuesday: 期中考 Finish up EM
未教MANOVA, Profile analysis, and growth curves |
第11週 |
5/03, 5/05 |
Tuesday & Thursday: EM algorithm and Likelihood Ratio test |
第12週 |
5/10, 5/12 |
Tuesday: EM algorithm and Multivariate Normal Distribution) |
第13週 |
5/17, 5/19 |
Tuesday: Factor Analysis, Thursday: Support Vector Machine |
第14週 |
5/24, 5/26 |
Tuesday: Canonical Correlation Analysis, Thursday: Factor Analysis;
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第15週 |
5/31, 6/02 |
Monday: Canonical Correlation Analysis; Tuesday: Clustering |
第16週 |
6/07, 6/09 |
Tuesday and Thursday: Discrimination and Classification
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第17週 |
6/14, 6/16 |
Tuesday: VC class Thursday: Support Vector Machine |
第18週 |
6/21 |
Tuesday: Final (open book exam) |
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