AF: Small: Algorithms for Diverse and Fair Optimization

海量数据的可用性在广泛使用的机器学习算法的发展中发挥了关键作用。处理如此大量的数据的一个主要挑战是如何挑选出代表整体但可以在这些算法中有效使用的较小部分。该项目旨在找到新的模型和算法，以识别给定数据集合中一小部分但具有代表性的部分。该项目还将考虑数据识别和表示方面的公平问题。PI将把这一项目的成果纳入本科生和研究生的课程开发活动。该项目还将涉及对本科生和研究生的培训，特别是对STEM中代表性不足群体的培训。国际和平协会还将在各种外联活动中向包括K-12学生在内的更广泛的受众介绍该项目的挑战和成果。该项目旨在引入和开发一个在子集选择问题中对多样性进行建模的通用框架。总体框架涵盖了各种领域的问题，包括机器学习中的行列式点过程、线性回归的最优设计、公平和有效的商品分配，以及网络设计问题。该项目旨在通过共同的视角对这些广泛的主题进行研究，从而带来算法上的进步。该项目的第二个密切相关的重点是研究数据的公平表示，特别是在降维算法中，随着数据在社会中的普遍使用，降维算法变得越来越重要。在这个问题上的算法观点与该项目旨在调查的半定程序的极点的结构密切相关，并开发一个算法框架来概括PI在线性程序上的工作。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 availability of enormous quantities of data has played a crucial role in the development of widely used machine-learning algorithms. A major challenge with this large quantity of data is how to pick out a smaller part that is representative of the whole but can be efficiently used in these algorithms. The project aims to find new models and algorithms to identify a small but representative part of a given collection of data. Fairness aspects in identification as well as representation of data will also be considered in the project. The PI will incorporate results from this project into curriculum-development activities at both the undergraduate and graduate level. The project will also involve training of undergraduate and graduate students, especially from underrepresented groups in STEM. The PI will also talk about the challenges and the results of the project to a wider audience, including K-12 students, at various outreach events. The project aims to introduce and develop a general framework for modeling diversity in subset-selection problems. The general framework encompasses problems froma variety of areas including determinantal point processes in machine learning, optimal design for linear regression, fair and efficient allocation of goods, and network-design problems. The project intends to bring algorithmic advances on these wide-ranging topics by studying them through a common lens. A second closely related focus of this project is to study fair representation of data, especially in algorithms for dimensionality reduction, which is increasingly important with the pervasive use of data in society. The algorithmic viewpoint on this problem is closely related to the structure of extreme points of semidefinite programs that the project aims to investigate and to develop an algorithmic framework generalizing the PI's work on linear programs.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.