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

在过去的几十年里，数据集领域的智能数据分析发生了前所未有的巨大变化。大数据的分析计算量大，资源匮乏，而且更加复杂。 随着最近出现的应用，大多数研究的目标函数已被证明是非次模或非线性。此外，由于数十亿级数据集中存在动态，例如项目以在线方式到达，因此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。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科普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，许多新兴应用对智能大数据分析的重视。因此，该项目的成功在几乎所有需要轻量级和接近最佳大数据分析的领域都具有很高的影响力。该项目的研究成果也将丰富网络科学、图论、优化和大数据分析的研究。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。针对代表性不足的群体和K-1的推广活动该项目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约束保证，用于非子模块和非线性优化。特别是，该项目为新的数据挖掘技术奠定了基础，适用于具有新兴应用的大数据新时代，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，非子模最大化类，这是许多新兴应用的基础。2)尝试将非线性优化与组合优化相结合的一个新的研究方向，从而为非子模优化的研究带来新的视角，加深对问题结构的理解。3)新颖的基于流的主动挖掘在多个应用程序的规模，集中在两个通用模型，统一在线社交网络和隐私领域的许多优化问题。它还提供了一个新的理论框架，自适应非子模最大化，这还没有在文献中研究。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程序，将弥合理论与实践之间的差距。该奖项反映了NSF的法定使命，并被认为值得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来支持。

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.