CIF: Small: Collaborative Research: Scalable Nonconvex Optimization with Statistical Guarantees for Information Computing in High Dimensions

点击翻译按钮获取中文摘要

The data explosion in all fields of science recently creates an urgent need for methodologies for analyzing high dimensional data with low-dimensional structure. The research, devoted to developing transformative theory and methods for scalable nonconvex optimization with statistical guarantees in noisy settings, has applications in a wide range of disciplines such as signal processing, machine learning, operations research, and computer vision. The investigators propose methodologies of statistics-guided nonconvex optimization and optimization-assisted statistical analysis to study convergence rate, acceleration, and statistical accuracy of iterative nonconvex algorithms for signals with mixed types of structural parsimony. The project cross-fertilizes ideas from statistics, operations research, engineering, and computer science and has education tightly coupled with research. The integrated research and education help students develop critical thinking through cross-disciplinary training, and assist students in becoming life-long learners. The investigators use the rich topics in this project to inspire the learning and discovery interest of the public and students of all ages; in addition, the outreach activities help attract minority and female students to careers in science.The research performs statistical-accuracy guided algorithmic analysis of general majorization-minorization algorithms for fast and stable signal recovery. Scalable and randomized acceleration schemes are proposed and studied in big-data applications. The investigators develop an innovative optimization-based statistical methodology for analyzing multi-regularized sparse estimators in high dimensions. The project applies the techniques to robust principle component estimation, hierarchical modeling, network learning, among others. The research creates a fusion of optimization and statistics for information computing in high dimensions, and deepens and broadens existing compressed sensing and nonconvex optimization theories and methods.