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

我们现在生活在数据泛滥的时代。要处理的数据量之大，加上统计模型的日益复杂和数据来源日益分散的性质，给现代统计理论带来了新的挑战。标准的机器学习方法不再能够适应计算要求。它们需要重新设计或调整，这就需要针对海量数据的可伸缩学习算法的新一代设计和理论。该项目旨在为大数据分析提供一系列最先进的非参数学习工具，可供科学家和从业者直接使用，并对生物医学、医疗保健、国防与安全、信息技术等多个领域产生有益影响。该项目的可交付成果包括易于使用的软件包，这些软件包将通过一系列应用程序实例进行全面评估。它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，最初为单台机器设计的传统统计推理程序不再适用于现代大数据集。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的学习算法，或者如果只有一台机器可用，则以随机草图的方式进行。这些新算法的计算极限将从统计学的角度进行检验。例如，在分而治之的设置中，可以将部署的机器数量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：当这个数字低于这个上限时，就可以实现统计最优(就非参数估计或检验而言)；否则，统计最优就变得不可能了。相关问题也将在随机草图方法中以随机项目的最小数量来解决。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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computational bottlenecks, traditional statistical inferential procedures originally designed for a single machine are no longer applicable to modern large datasets.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.