AF: Small: Algorithms for Diverse and Fair Optimization

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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.