In the Big-Data era, there is a pressing need to develop more efficient and easy-to-interpret data analysis methods to face the new challenges rising from real life applications, such as cancer diagnosis, brain connectivity network and neuroimaging studies. Besides their intimidating sizes, data sets in such applications demand researchers to understand the intrinsic and complex structure behind them. This research involves new directions in discriminant analysis and classification by exploring state-of-art statistical methods and contemporary computation techniques. The investigators will develop new statistical methods and computational tools to utilize the intrinsic structure of the data, such as high correlation, network structure and tensor/array data structure. The research results will advance the research in statistics, machine learning, text mining, bio-medical research, finance, neuroimaging analysis, among other fields. The research will also be integrated with substantial educational and outreach activities.
In this research, the investigators aim to develop parsimonious probabilistic discriminant analysis models for efficiently analyzing data with intrinsically complicated structures, and for improved estimation of parameters and accuracy in predictions. Three sets of problems will be investigated: (1) parsimonious linear discriminant analysis with envelope, aiming to integrate a nascent technique of envelope modeling with the classical linear discriminant analysis model; (2) simultaneous discriminant analysis and differential network estimation, aiming to develop a novel and unified framework for simultaneously studying differential networks, estimating multiple covariance matrices, and training quadratic discriminant analysis classifier; and (3) sparse tensor discriminant analysis with feature selection, aiming to develop a sparse discriminant analysis method for tensor-valued data that directly uses the tensor-valued features for discriminant analysis, while simultaneously achieving feature selection and preserving interpretable tensor structure.