CDS&E: Collaborative Research: Scalable Nonparametric Learning for Massive Data with Statistical Guarantees

CDS

• 批准号: 1821157
• 负责人: Zuofeng Shang
• 金额: $ 15.5万
• 依托单位: Indiana University
• 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: 2018-08-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1821157&HistoricalAwards=false
• 关键词: CDS& Collaborative; Research; Scalable; Nonparametric

We now live in the era of data deluge. The sheer volume of the data to be processed, together with the growing complexity of statistical models and the increasingly distributed nature of the data sources, creates new challenges to modern statistics theory. Standard machine learning methods are no longer able to accommodate the computational requirements. They need to be re-designed or adapted, which calls for a new generation of design and theory of scalable learning algorithms for massive data. This project aims to provide a collection of state-of-the-art nonparametric learning tools for big data analysis, which can be directly used by scientists and practitioners and have beneficial impacts on various fields such as biomedicine, health-care, defense and security, and information technology. The deliverables of this project include easy-to-use software packages that will be thoroughly evaluated using a range of application examples. They will directly help scientists to explore and analyze complex data sets. Due to storage and computational bottlenecks, traditional statistical inferential procedures originally designed for a single machine are no longer applicable to modern large datasets. This project aims to design new scalable learning algorithms of wide-ranging nonparametric models for data that are distributed across a large number of multi-core computational nodes, or in a fashion of random sketching if only a single machine is available. The computational limits of these new algorithms will be examined from a statistical perspective. For example, in the divide-and-conquer setup, the number of deployed machines can be viewed as a simple proxy for computing cost. The project aims to establish a sharp upper bound for this number: when the number is below this bound, statistical optimality (in terms of nonparametric estimation or testing) is achievable; otherwise, statistical optimality becomes impossible. Related questions will also be addressed in the randomized sketching method in terms of the minimal number of random projections.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.

我们现在生活在数据洪流的时代。需要处理的数据量巨大，加上统计模型的日益复杂性和数据源日益分散的性质，给现代统计理论带来了新的挑战。标准机器学习方法不再能够满足计算要求。它们需要重新设计或调整，这就需要针对海量数据的新一代可扩展学习算法的设计和理论。该项目旨在提供一系列最先进的大数据分析非参数学习工具，可供科学家和从业者直接使用，并对生物医学、医疗保健、国防和安全等各个领域产生有益影响和信息技术。该项目的交付成果包括易于使用的软件包，将使用一系列应用示例对其进行彻底评估。他们将直接帮助科学家探索和分析复杂的数据集。由于存储和计算瓶颈，最初为单机设计的传统统计推理程序不再适用于现代大型数据集。该项目旨在为分布在大量多核计算节点上的数据设计新的可扩展的非参数模型学习算法，或者在只有一台机器可用的情况下以随机草图的方式设计。这些新算法的计算限制将从统计角度进行检验。例如，在分而治之的设置中，部署的机器数量可以被视为计算成本的简单代理。该项目旨在为这个数字建立一个明确的上限：当数字低于这个界限时，可以实现统计最优性（在非参数估计或测试方面）；否则，统计最优性就不可能实现。相关问题也将在随机草图方法中根据最小数量的随机预测得到解决。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Distributed Generalized Cross-Validation for Divide-and-Conquer Kernel Ridge Regression and Its Asymptotic Optimality

• DOI: 10.1080/10618600.2019.1586714
• 发表时间: 2016-12
• 期刊: Journal of Computational and Graphical Statistics
• 影响因子: 2.4
• 作者: Ganggang Xu;Zuofeng Shang;Guang Cheng

Optimal Tuning for Divide-and-conquer Kernel Ridge Regression with Massive Data

• 发表时间: 2016-12
• 作者: Ganggang Xu;Zuofeng Shang;Guang Cheng

Estimation of the mean function of functional data via deep neural networks

通过深度神经网络估计功能数据的均值函数

• DOI: 10.1002/sta4.393
• 发表时间: 2021
• 期刊: Stat
• 影响因子: 1.7
• 作者: Wang, Shuoyang;Cao, Guanqun;Shang, Zuofeng;for the Alzheimer's Disease Neuroimaging Initiative
• 通讯作者: for the Alzheimer's Disease Neuroimaging Initiative