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).