III: Small: Collaborative Research: Stream-Based Active Mining at Scale: Non-Linear Non-Submodular Maximization

在过去的几十年里，智能数据分析在数据集领域以前所未有的规模发生了巨大的变化。大数据分析需要大量的计算、大量的资源，而且要复杂得多。随着最近新兴的应用，大多数研究的目标函数已经被证明是非子模或非线性的。此外，随着亿级数据集中存在动态变化，例如物品以在线方式到达，必须研究可伸缩的基于流的自适应算法，这种算法可以快速更新解，而不是从头开始重新计算。所有上述问题都需要一种可扩展的、基于流的主动挖掘技术来应对大数据时代非子模块最大化的巨大应用。随着社会对网络空间和计算机技术的日益依赖，许多新兴应用的智能大数据分析受到了重视。因此，该项目的成功几乎在任何需要轻量级和近乎最优的大数据分析的领域都具有很高的影响。该项目的研究成果还将丰富网络科学、图论、优化、大数据分析等方面的研究。除了开设新课程外，本科生和高中生还将在实验平台上参与动手活动。针对代表性不足的群体和K-1的外联活动本项目为非子模块和非线性优化类别开发了一个理论框架，以及高度可扩展的近似算法和严格的理论性能界限保证。特别是，该项目为适应大数据和新兴应用的新时代的新型数据挖掘技术奠定了基础，并推进了随机和基于流的算法设计的研究前沿，具有几个关键创新：1)严格的数学技术来分析和设计高度可扩展的近似算法，以非单调、非子模最大化的类为基础，这是许多新兴应用的基础。2)将非线性优化问题与组合优化问题相结合，尝试了一个新的研究方向，为非子模块优化问题的研究带来了新的视角，加深了对问题结构的理解。3)提出了一种基于流的大规模多应用主动挖掘算法，重点研究了在线社交网络和隐私领域的两个通用模型，将众多的优化问题统一起来。它还为自适应非子模极大化提供了一个新的理论框架，这在文献中还没有被研究过。4)通过各种工具和方法的组合进行广泛的评估，包括将理论和实践之间的差距架起桥梁的真实世界数据集和应用程序。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。

The past decades have witnessed enormous transformations of intelligent data analysis in the realm of datasets at an unprecedented scale. Analysis of big data is computationally demanding, resource hungry, and much more complex. With recent emerging applications, most of the studied objective functions have been shown to be non-submodular or non-linear. Additionally, with the presence of dynamics in billion-scale datasets, such as items are arriving in an online fashion, scalable and stream-based adaptive algorithms which can quickly update solutions instead of recalculating from scratch must be investigated. All of the aforementioned issues call for a scalable and stream-based active mining techniques to cope with enormous applications of non-submodular maximization in the era of big data. With the society's growing dependence on the cyberspace and computer technologies, the premium placed on the intelligent big data analysis for many emerging applications. Therefore, the success of this project has a high impact in almost any field that needs lightweight and near-optimal big data analysis. The findings of this project will also enrich the research on network science, graph theory, optimization, and big data analysis. In addition to creating new courses, undergrad and high school students will be involved in hands-on activities over the experimental platform. Outreach events targeted at under-represented groups and K-1This project develops a theoretical framework together with highly scalable approximation algorithms and tight theoretical performance bound guarantees for the class of non-submodular and non-linear optimization. In particular, the project lays the foundation for the novel data mining techniques, suitable to the new era of big data with emerging applications, as well as advance the research front of stochastic and stream-based algorithm designs, with several key innovations: 1) Rigorous mathematical techniques to analyze and design highly scalable approximation algorithms to the class of non-monotonic, non-submodular maximization, which underlies many emerging applications. 2) Attempt a new research direction by bridging the non-linear optimization and the combinatorial optimization, thereby bringing the new angles for the study of non-submodular optimization as well as getting deeper understanding of the problem structures. 3) Novel stream-based active mining at scale for multiple applications, focused on the two general models which unify many optimization problems in the domain of online social networks and privacy. It also provides a novel theoretical framework for adaptive non-submodular maximization, which has not been studied in the literature. 4) Extensive evaluation through a combination of various tools and methods, including the real-world datasets and applications that will bridge the gap between theory and practice.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.