CAREER: Theory and Methods for Simultaneous Variable Selection and Rank Reduction

Florida State University, Tallahassee FL

Investigators

Abstract

The data explosion in all fields of science creates an urgent need for methodologies for analyzing high dimensional multivariate data. The project deepens and broadens existing sparsity and low rank statistical theories and methods by making the following major scientific achievements: (a) an innovative selectable reduced rank methodology through simultaneous variable selection and projection, with guaranteed lower error rate than existing variable selection and rank reduction rates in theory, which paves the way to new frontiers in high dimensional statistics and information theory; (b) fast but simple-to-implement algorithms that can deal with all popular penalty functions (possibly nonconvex) in computation with guaranteed global convergence and local optimality, to ensure the practicality of the proposed approaches in big data applications; (c) a generic extension to non-Gaussian models capable of taking into account the correlation between multivariate responses, with a universal algorithm design based on manifold optimization; (d) a unified robustification scheme that can both identify and accommodate gross outliers occurring frequently in real data, to overcome the non-robustness of many conventional multivariate tools; (e) general-purpose model selection methods serving variable selection and/or rank reduction and achieving the finite-sample optimal prediction error rate with theoretical guarantee. The need to recover low-dimensional signals from high dimensional multivariate noisy data permeates all fields of science and engineering. Hence a project of this nature, designed to develop transformative theory and methods for simultaneous variable selection and rank reduction, finds applications in a wide range of disciplines and areas such as machine learning, signal processing, and biostatistics, among others. By cross-fertilizing ideas from statistics, mathematics, engineering, and computer science, the integrated research and education help students develop critical thinking through cross-disciplinary training, and assist students in becoming life-long learners. The investigator uses the rich topics in this project to inspire the learning and discovery interest of the public and students of all ages. The educational plan consists of course development, student mentoring, outreach, and recruiting underrepresented students.