課程名稱 |
統計模型降維 Dimension Reduction in Statistical Modeling |
開課學期 |
102-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
李克昭 |
課號 |
MATH5605 |
課程識別碼 |
221 U6320 |
班次 |
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學分 |
2 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四1,2(8:10~10:00) |
上課地點 |
天數304 |
備註 |
與陳 宏合開 總人數上限:30人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1022MATH5605_dim |
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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課程概述 |
Statistical data analysis is an extremely versatile area. Among the various aspects involved, this course will focus on dimension reduction, an issue that can arise in every scientific field.
Dimensionality is an issue that can arise in every scientific field. Generally speaking,
the difficulty lies on how to visualize a high dimensional function or data set. People often ask : "How do they look?", "What structures are there?", "What model should be used?" Aside from the differences that underlie the various scientific contexts, such kind of questions do have a common root in Statistics. This is the driving force for the study of high dimensional data analysis.Dimension reduction can find roots in topics ranging from classical multivariate analysis to modern machine learning or data mining techniques. This course will place more emphasis on a dimension reduction theory that links forward regression with inverse regression. As the era of big data arrives, this course will equip students with the enabling statistical tools to analyze the real-world data in a disciplined manner.
This course will discuss several statistical methodologies useful for exploring voluminous data. They include Principal Component Analysis, Clustering and Classification, Tree-structured analysis, Neural Network, Hidden Markov Models, Sliced inverse regression(SIR) and principal Hessian direction(PHD).
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課程目標 |
Serve as an impetus of stimulating more ideas on how to model data arising from complex systems of
very large dimensions. |
課程要求 |
No Exam.
Final Report, presentation and participation of in-class discussion. |
預期每週課後學習時數 |
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Office Hours |
每週三 09:00~11:00 每週四 10:00~11:00 備註: 1 Professor Li's office hour 2 Professor Chen's office hour |
指定閱讀 |
None. Instructor's lecture notes will be available. Selected papers for reading will be assigned. |
參考書目 |
High dimensional data analysis via the SIR/PHD approach (2000) by Ker-Chau Li (李克昭教授).
The note can be downloaded. (http://www.stat.ucla.edu/~kcli/sir-PHD.pdf)
Selected papers for reading will be assigned. |
評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
第1週 |
2/20 |
Parametric, nonparametric, and semiparametric regression; analysis of variance and covariance |
第2週 |
2/27 |
Transformation, principal Component analysis projection pursuit, Classification |
第3週 |
3/06 |
Support vector machine; clustering; neural network. |
第4週 |
3/13 |
Sliced inverse regression, Sampling property of Sliced inverse regression |
第5週 |
3/20 |
Sampling property of Sliced inverse regression, application. |
第6週 |
3/27 |
Sliced Inverse Regression : Basics |
第7週 |
4/03 |
Sampling properties of SIR and Applications |
第8週 |
4/10 |
Transformation |
第9週 |
4/17 |
Second moment based methods |
第10週 |
4/24 |
Principal Hessian Directions |
第11週 |
5/01 |
Linear design condition |
第12週 |
5/08 |
Nonlineary confounding |
第13週 |
5/15 |
Errors in regressor variables and censored regression |
第14週 |
5/22 |
Selective topics from recent development I |
第15週 |
5/29 |
Selective topics from recent development II |
第16週 |
6/05 |
Selective topics from recent development III
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