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

在过去的几十年里，智能数据分析以前所未有的规模在数据集领域发生了巨大的转变。对大数据的分析需要大量的计算、大量的资源，而且要复杂得多。随着近年来的应用，大多数研究的目标函数已被证明是非次模或非线性的。此外，由于数十亿规模的数据集中存在动态，例如以在线方式到达的项目，必须研究可扩展和基于流的自适应算法，这些算法可以快速更新解决方案，而不是从头开始重新计算。上述所有问题都需要一种可扩展的、基于流的主动挖掘技术，以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，智能大数据分析在许多新兴应用中受到重视。因此，这个项目的成功对几乎所有需要轻量级和接近最佳的大数据分析的领域都有很大的影响。本项目的研究成果也将丰富网络科学、图论、优化、大数据分析等方面的研究。除了创建新课程外，本科生和高中生还将参与实验平台上的实践活动。针对代表性不足群体和k -1的外展活动。该项目为非子模块和非线性优化类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新时代新兴应用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，具有以下几个关键创新：1)严格的数学技术，用于分析和设计高度可扩展的近似算法，以实现非单调，非次模最大化，这是许多新兴应用的基础。2)通过将非线性优化与组合优化相结合，尝试了新的研究方向，为非次模优化的研究带来了新的角度，对问题结构有了更深入的认识。3)针对多应用的基于流的新型大规模主动挖掘，重点研究了两种通用模型，该模型统一了在线社交网络和隐私领域的许多优化问题。它还为自适应非次模最大化提供了一个新的理论框架，这在文献中还没有研究过。4)通过各种工具和方法的组合进行广泛的评估，包括现实世界的数据集和应用，这将弥合理论与实践之间的差距。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。

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.