Efficient Algorithms for Fair and Diverse Subset Selection from High-Dimensional Data

Core Concepts

The authors develop the first constant approximation algorithm for the Fair Max-Min Diversification (FairDiv) problem that runs in near-linear time using only linear space. Their approach employs a novel combination of the Multiplicative Weight Update method and advanced geometric data structures to implicitly and approximately solve a linear program.

Abstract

The paper focuses on the problem of fair and diverse subset selection from high-dimensional data, known as the Fair Max-Min Diversification (FairDiv) problem. The key contributions are: MFD Algorithm: The authors present the MFD algorithm, the first constant approximation algorithm for FairDiv that runs in near-linear time using only linear space. Previous constant approximation algorithms had super-linear running time and space. MFD Algorithm with High Probability Fairness: The authors extend the MFD algorithm to satisfy the fairness constraints with high probability, by solving a modified linear feasibility problem. Coreset Construction: The authors show that any algorithm for the k-center clustering problem can be used to derive a (1+ε)-coreset for the FairDiv problem efficiently. Using this coreset, they propose the first efficient streaming algorithm for FairDiv. Range Query Algorithm: The authors design a data structure that can efficiently return a fair and diverse subset of points within a given query region. The algorithms use a novel combination of the Multiplicative Weight Update method and advanced geometric data structures, such as BBD-trees, to implicitly and approximately solve the linear programs underlying the FairDiv problem.

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Faster Algorithms for Fair Max-Min Diversification in $\mathbb{R}^d$

by Yash Kurkure... at arxiv.org 04-09-2024

https://arxiv.org/pdf/2404.04713.pdf

Deeper Inquiries

How can the proposed techniques be extended to handle dynamic data, where the input points are continuously added or removed over time

The proposed techniques can be extended to handle dynamic data by incorporating incremental updates and maintaining a summary of the data points encountered so far. When a new point is added, the algorithm can update the summary statistics and adjust the solution accordingly. Similarly, when a point is removed, the algorithm can recompute the solution based on the updated data set. By efficiently updating the internal data structures and maintaining fairness constraints, the algorithm can adapt to changes in the input data over time.

Can the algorithms be adapted to handle other notions of fairness beyond group fairness, such as individual fairness or intersectional fairness

The algorithms can be adapted to handle other notions of fairness beyond group fairness by modifying the constraints and objectives in the optimization problem. For individual fairness, the algorithm can ensure that similar individuals are treated similarly in the subset selection process. This can be achieved by incorporating distance metrics or similarity measures between data points. For intersectional fairness, the algorithm can consider multiple sensitive attributes simultaneously and ensure that the selected subset is diverse and representative across all intersections of these attributes.

What are the potential applications of the fair and diverse subset selection techniques beyond the examples discussed in the paper, and how could they impact real-world decision-making processes

The fair and diverse subset selection techniques have a wide range of potential applications beyond the examples discussed in the paper. These techniques can be applied in various domains such as hiring practices, loan approvals, criminal justice, and healthcare. By ensuring fairness and diversity in decision-making processes, these algorithms can help mitigate biases and promote inclusivity. For example, in hiring practices, the algorithms can assist in selecting a diverse pool of candidates from different backgrounds and experiences. In healthcare, the algorithms can aid in patient selection for clinical trials to ensure representation across various demographic groups. Overall, the impact of these techniques lies in promoting fairness, equity, and diversity in critical decision-making processes.