100年第1學期-4849 高維度資料分析 課程資訊
本課程介紹多個創新多變量統計方法(例如: 反切迴歸、Principal Hessian Directions與MAVE等),用以達到資料縮減(data reduction)的目的。
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.
Office HourOffice hours: Mon. 16:10-17:00、Tue. 11:10-12:00、Wed. 09:10-10:00、Thurs. 11:10-12:00. Classroom: will be announced.
No textbook. Lecture notes and selected papers will be available.