課程大綱

課程資訊

課程名稱

多變量統計分析
Multivariates Statistical Analysis

開課學期

107-2

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

學分

3.0

全/半年

半年

必/選修

必修

上課時間

星期一8,9(15:30~17:20)星期二8(15:30~16:20)

上課地點

天數101天數101

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/1072MATH7610_MVA

課程簡介影片

核心能力關聯

本課程尚未建立核心能力關連

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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

Office Hours

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]

參考書目

Flury, B. (1997) A First Course In Multivariate Statistics. Springer.
Srivastava, M. S. (2002) Methods of Multivariate Statistics. Wiley

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Quiz	10%
2.	Final/Project	30%
3.	Midterm	30%
4.	Homework	30%

課程進度

週次	日期	單元主題
第1週	2/18, 19	Tuesday & Wednesday: 4V in Big Data, PageRank, Graph, and Social Network; Random projection on reduce amount of data
第2週	2/25, 26	Tuesday: Talk about Random Projection.
第3週	3/04, 05	Tuesday: population PCA, functional data Thursday: Multivariate Normal distribution; Matrix Algebra and Random Vectors
第4週	3/11, 13	Tuesday and Thursday: Chapter 4.2 Multivariate Normal Density and Its Properties Ch4.3 Estimation in MVN
第5週	3/18, 19	Tuesday: Derive MLE and finish up Chapter 4.3-4.6 Thursday: Finish Chapter 4.
第6週	3/25, 26	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)
第7週	4/01, 02	factor analysis
第8週	4/08, 09	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
第9週	4/15, 16	Tuesday: 期中考 Finish up EM 未教MANOVA, Profile analysis, and growth curves
第11週	4/29, 30	Tuesday & Thursday: EM algorithm and Likelihood Ratio test
第12週	5/06, 07	Tuesday: EM algorithm and Multivariate Normal Distribution) classification
第13週	5/13, 14	Tuesday: Factor Analysis, Thursday: Support Vector Machine
第14週	5/20, 21	Tuesday: Canonical Correlation Analysis, Thursday: Factor Analysis;
第15週	5/27, 28	Monday: Canonical Correlation Analysis; Tuesday: Clustering
第16週	6/03, 04	Tuesday and Thursday: Discrimination and Classification; recursive partition http://www.stat.cmu.edu/~cshalizi/350-2006/lecture-10.pdf
第17週	6/10, 11	Tuesday: VC class Thursday: Support Vector Machine
第18週	6/18	Tuesday: Final (open book exam)