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

CIF：小型：协作研究：具有统计保证的可扩展非凸优化，用于高维信息计算

• 批准号: 1617801
• 负责人: Yiyuan She
• 金额: $ 28.5万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1617801&HistoricalAwards=false
• 关键词: CIF; Small; Collaborative; Research; Scalable

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.

最近，所有科学领域的数据爆炸迫切需要用低维结构分析高维数据的方法。该研究致力于开发可扩展的非凸优化的变革性理论和方法，并在噪声环境中提供统计保证，在信号处理、机器学习、运筹学和计算机视觉等广泛学科中得到应用。研究人员提出了统计引导的非凸优化和优化辅助统计分析的方法，以研究具有混合类型结构简约的信号的迭代非凸算法的收敛速度、加速和统计精度。该项目融合了统计学、运筹学、工程和计算机科学的思想，并将教育与研究紧密结合。 一体化的研究和教育通过跨学科训练帮助学生培养批判性思维，帮助学生成为终身学习者。研究者利用本项目丰富的主题激发公众和各年龄段学生的学习和发现兴趣；此外，外展活动有助于吸引少数族裔和女学生从事科学事业。该研究对一般大化-小化算法进行统计精度引导的算法分析，以实现快速稳定的信号恢复。在大数据应用中提出并研究了可扩展和随机的加速方案。研究人员开发了一种基于优化的创新统计方法，用于分析高维的多重正则化稀疏估计量。该项目将这些技术应用于鲁棒主成分估计、分层建模、网络学习等。 该研究创造了高维信息计算的优化和统计的融合，深化和拓宽了现有的压缩感知和非凸优化理论和方法。