Collaborative Research: New Methods, Theory and Applications for Nonsmooth Manifold-Based Learning

协作研究：非平滑流形学习的新方法、理论和应用

• 批准号: 2243650
• 负责人: Shiqian Ma
• 金额: $ 15万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-10-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2243650&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Methods; Theory

Massive high-dimensional data are ubiquitous in many scientific and engineering disciplines, such as bioinformatics, computer vision, neuroimaging, and signal processing. This proposal is motivated by emerging tools for analyzing data from these disciplines, such as nonsmooth, manifold-based learning with high-dimensional and multidimensional data. Building on the synergy among statistics, machine learning, and optimization, this research will focus on the development of new optimization algorithms and theory for nonsmooth manifold optimization. The project will also build on existing optimization strengths to develop new methods and theory in statistics and machine learning. Software packages will be developed to make the research outcomes readily available to other researchers and practitioners. In addition, the project will enhance the future technical workforce through the training of graduate students. It is known that statistical modeling of high-dimensional data may include the non-smooth regularization in the objective function, and some may even involve non-convex manifold constraints such as orthogonality constraints. The manifold-based learning offers a powerful framework for dimension reduction and signal processing. The combination of non-smooth regularization and non-convex manifold constraints brings new opportunities and challenges for designing optimization algorithms with convergence guarantees and also for developing new statistical methods and theory. The research outcomes of this project will provide new powerful analytic tools in nonsmooth manifold-based learning with theoretical guarantees. Software packages will be developed to make the research outcomes readily available to other researchers and practitioners.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.

大量的高维数据在许多科学和工程学科中无处不在，例如生物信息学，计算机视觉，神经成像和信号处理。该提案是由用于分析这些学科的数据的新兴工具的动机，例如使用高维和多维数据的非平滑，基于多方面的学习。在统计，机器学习和优化之间的协同作用的基础上，这项研究将着重于开发新的优化算法和非平滑歧管优化的理论。该项目还将基于现有的优化优势，以开发统计和机器学习中的新方法和理论。将开发软件包，以使其他研究人员和从业者可以轻松地获得研究成果。此外，该项目将通过培训研究生来增强未来的技术劳动力。众所周知，高维数据的统计建模可能包括目标函数中的非平滑正则化，有些甚至可能涉及非凸流歧管约束，例如正交性约束。基于多种的学习为缩小维度和信号处理提供了强大的框架。非平滑正则化和非凸流歧管约束的结合带来了新的机会和挑战，可以通过融合保证设计优化算法以及开发新的统计方法和理论。该项目的研究成果将在基于理论保证的基于非平滑歧视的学习中提供新的强大分析工具。将开发软件包，以使其他研究人员和从业人员容易获得研究成果。该奖项反映了NSF的法定任务，并认为使用基金会的知识分子优点和更广泛的影响评估标准，认为值得通过评估来获得支持。