學習多變量降維方法於統計實務的應用分析。本課程介紹多個創新的統計降維方法(例如:分段逆迴歸法(Sliced Inverse Regression)、主要黑森定向法(principal Hessian Directions)等)，用以達到資料縮減(data reduction)的目的，並且應用至大量資料集。
A Tentative Course Outline :
Week 1 : 迴歸分析之維度縮減模型；主成份分析(PCA)
Week 2-3 : 分段逆迴歸法 (SIR)及其應用
Week 4-5 : 主要黑森定向法 (PHD)
Week 6 : 非線性擾動迴歸 (Nonlinear Confounding)
Week 7 : 測量誤差 (Error in Regressors)
Week 8 : 變異數之因子分析 (ANOVA Factorial Analysis)
Week 9 : 期中報告
Week 10-11 : 設限迴歸 (Censored Regression)
Week 12 : 樹狀迴歸 (Tree-structured Regression)
Week 13-14 : 多變項反應變數迴歸 (Multivariate Outcome Data)
Week 15-16 : 廣義線性區別分析 (Generalization Fisher LDA)
Week 17 : 手寫辨識 (Handwritten digit Recognition)
Week 18 : 期末報告Learn the application analysis of the multi-variable reduction method in statistical practice. This course introduces several innovative statistical reduction methods (such as Sliced Inverse Regression, principal Hessian Directions, etc.) to achieve the purpose of data reduction and apply to a large number of data sets.
A Tentative Course Outline:
Week 1: Dimension reduction model for replication analysis; principal component analysis (PCA)
Week 2-3: Segmented Inverse Reversal Method (SIR) and Its Application
Week 4-5: Main Hessian Directional Method (PHD)
Week 6: Nonlinear Confounding
Week 7: Error in Regressors
Week 8: ANOVA Factorial Analysis
Week 9: Midterm Report
Week 10-11: Censored Regression
Week 12: Tree-structured Regression
Week 13-14: Multivariate Outcome Data
Week 15-16: Generalization Fisher LDA
Week 17: Handwritten digit Recognition
Week 18: Final Report
The reduction of dimension 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 kinds of questions do have a common root in Statistics. This is the driving force for the study of high dimensional data analysis. This course will discuss several statistical methodologies useful for exploring voluminous data. They include principal component analysis, clustering and classification, survival analysis and other recent developed sufficient dimension reduction (SDR) methods. Sliced inverse regression (SIR) and principal Hessian direction (PHD) are two novel SDR methods, useful for the extraction of geometric information underlying noisy data of several dimensions. The theories of several SDR methods will be discussed in depth. They will be used as the backbone for the entire course. Examples from various application areas will be given. They include social/economic problems like unemployment rates, biostatistics problems like clinic trials with censoring, machine learning problems like handwritten digital recognition, biomedical problems like functional Magnet Resonance Imaging, and bioinformatics problems like micro-array gene expression etc.
The reduction of dimension 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 kinds of questions do have a common root in Statistics. This is the driving force for the study of high dimensional data analysis. This course will discuss several statistical methods useful for exploring volumetric data. They include principal component analysis, clustering and classification, survival analysis and other recent developed sufficient dimension reduction (SDR) methods. Sliced inverse regression (SIR) and principal Hessian direction (PHD) are two novel SDR methods, useful for the extraction of geometric information underlying noisy data of several dimensions. The theories of several SDR methods will be discussed in depth. They will be used as the backbone for the entire course. Examples from various application areas will be given. They include social/economic problems like unemployment rates, biostatistics problems like clinical trials with censoring, machine learning problems like handwritten digital recognition, biomedical problems like functional Magnet Resonance Imaging, and bioinformatics problems like micro-array gene expression etc.
No textbook. Lecture notes and selected papers will be available.
No textbook. Lecture notes and selected papers will be available.
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