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；主成份分析 (PCA)
Week 2-3 : 分段逆迴歸法 (SIR)
Week 4-5 : 設限迴歸 (censored regression)
Week 6-7 : 主要黑森定向法 (PHD)
Week 8 : 多變項反應變數迴歸：Most Predictable Variables
Week 9 : 期中報告
Week 10-11 : 泛函資料分析 (functional data analysis)
Week 12-13 : 超高維之變數選取
Week 14: 最小平均變異估計法：MAVE
Week 15-17: 其他多變量方法: LASSO
Week 18 : 期末報告

Learn the application analysis of multi-variable dimensionality reduction methods in statistical practice. This course introduces a number of innovative statistical dimensionality reduction methods (such as Sliced ​​Inverse Regression, principal Hessian Directions, etc.) to achieve the purpose of data reduction and apply them to a large number of data sets.
A Tentative Course Outline:
Week 1: Dimensionality reduction in regression analysis; Principal Component Analysis (PCA)
Week 2-3: Segmented Inverse Regression (SIR)
Week 4-5: censored regression
Week 6-7 : Main Hessian Orientation (PHD)
Week 8: Multivariate Response Variable Regression: Most Predictable Variables
Week 9: Interim report
Week 10-11: Functional data analysis (functional data analysis)
Week 12-13: Super high-dimensional variable selection
Week 14: Minimum Mean Variation Estimation Method: MAVE
Week 15-17: Other multivariate methods: LASSO
Week 18: Final report

No textbook. Lecture notes and selected papers will be available.

No textbook. Lecture notes and selected papers will be available.