High-dimensional statistical learning and inference

Princeton University, Princeton NJ

Investigators

Abstract

The challenge of high-dimensionality characterizes many contemporary statistical problems arising from many frontiers of scientific research and technological development. In high-dimensional statistical research, low-dimensional structures, which entail sparsity under suitable parametrization, are needed to be explored in order to circumvent the issue of noise accumulation with dimensionality. This proposal intends to confront a number of important high-dimensional statistical problems from genomics, machine learning, health studies, economics, 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 and clustering from high-dimensional feature spaces; high-dimensional covariance matrix estimation for asset allocation and portfolio management; sparse covariance estimation for spatial and temporal studies and genetic networks. 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. These emerging problems of high societal impacts will be confronted via developing new statistical methods to address the features and challenges associated with high-dimensionality, from statistical computation, feature selection, to noise reduction. At the same time, the PI also intends to provide fundamental understanding, via asymptotic analysis and simulation studies, to these problems and their associated methodologies that push theory, methods, and computation forward. Thanks to technological innovation, the availability of large-scale and complex data are widely available nowadays in many contemporary scientific problems. High-dimensional statistical models are required to address these scientific endeavors. The challenges of high-dimensionality arise from diverse fields of sciences and the humanities, ranging from genomics and health sciences to economics and finance. In these fields, variable selection, feature extraction, sparsity explorations are crucial for knowledge discovery. In this proposal, we propose to develop cutting-edge statistical theory and methods to address these problems from genomic studies, machine learning, health science, economics, and finance. The proposed techniques and results will not only help researchers to solve emerging problems in their disciplines, but also have strong impact on statistical thinking, methodological development, and theoretical studies.