ABSTRACT

Thanks to technological innovation, the availability of large-scale and complex data is widely available nowadays in many emerging scientific problems. The challenge of high-dimensionality characterizes many contemporary statistical problems from frontiers of scientific research and technological development. In high-dimensional statistical research, low-dimensional structures are needed to be explored in order to circumvent the issue of noise accumulation with dimensionality. The talk will cover a number of important high-dimensional statistical problems from genomics, machine learning, and finance. These include various emerging issues from the analysis of microarray data such as normalization, significance analysis, and disease classification; variable selection and feature extraction from high-dimensional statistical learning; sparse classification; high-dimensional covariance matrix estimation for asset allocation and portfolio management. All of these problems have their distinguished characters from the context of their applications, but nevertheless share similar challenges with high dimensionality and admit features of sparsity. The challenges of variable selection and feature extraction in high-dimensional space will be addressed.