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CRII: CIF: New Structure-Exploiting and Memory-Efficient Methods for Large-Scale Optimization and Data Analysis

CRII：CIF：用于大规模优化和数据分析的新结构利用和内存高效方法

基本信息

批准号：
1755705
负责人：
Paul Grigas
金额：
$ 17.5万
依托单位：
University of California-Berkeley
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1755705&HistoricalAwards=false
关键词：
CRII CIF New Structure Exploiting

项目摘要

Large-scale optimization methods have been paramount to the successes of recent applications of machine learning and data analysis in a wide variety of domains. At the same time, certain structural properties of statistical models, such as sparsity or low-rank structure, have proven to be crucial for obtaining meaningful and accurate results in high dimensions. In addition to being highly scalable to large datasets, some optimization algorithms have the desirable property that they directly promote the aforementioned valuable structural properties of models. This project involves developing, analyzing, and implementing novel optimization algorithms that have such beneficial structure-exploiting and also memory-efficiency properties. This project directly involves the mentoring of graduate students, as well as integration of research results into an undergraduate level machine learning course and a graduate level course in optimization and statistical learning.The foundation for this project is the Frank-Wolfe Method, a particular structure-exploiting first-order gradient optimization algorithm, and the related methodology of in-face directions. In-face directions automatically promote well-structured near-optimal solutions and have encouraging memory-efficiency properties. This research will investigate conditions whereby methods with in-face directions, as applied to convex relaxations of matrix completion and more general atomic norm regularization problems, are guaranteed to have a low memory footprint. Furthermore, this project will extend the reach of methods that incorporate in-face directions to new problem classes, including non-smooth objective functions, non-convex objective functions, and stochastic gradient estimates. The proposed optimization framework and in-face methodology applies very generally, and has potential for broader impact in several areas, including recommender systems, bioinformatics, customer segmentation, sentiment analysis, and medical imaging.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

大规模优化方法对于最近机器学习和数据分析在各种领域的应用的成功至关重要。同时，统计模型的某些结构性质，如稀疏性或低秩结构，已被证明是在高维上获得有意义和准确结果的关键。除了对大型数据集具有高度可扩展性外，一些优化算法还具有直接提升上述有价值的模型结构特性的理想特性。这个项目包括开发、分析和实现新的优化算法，这些算法具有这样有益的结构利用和内存效率特性。该项目直接涉及研究生的指导，并将研究成果整合到本科水平的机器学习课程和研究生水平的优化与统计学习课程中。本项目的基础是Frank-Wolfe方法，一种特殊的结构利用一阶梯度优化算法，以及面朝方向的相关方法。正面方向自动促进结构良好的接近最优的解决方案，并具有令人鼓舞的内存效率特性。本研究将探讨具有正面方向的方法，如应用于矩阵补全的凸松弛和更一般的原子范数正则化问题时，保证具有低内存占用的条件。此外，该项目将扩展包含正面方向的方法的范围到新的问题类别，包括非光滑目标函数，非凸目标函数和随机梯度估计。所提出的优化框架和面对面方法适用范围非常广泛，并有可能在几个领域产生更广泛的影响，包括推荐系统、生物信息学、客户细分、情感分析和医学成像。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。