Fair Diversity Maximization with Few Representatives

2025-06-09

AI Summary

This paper studies the fairness-constrained diversity maximization problem: selecting $k$ representative points from a multi-label dataset such that at most a constant number of samples is chosen from each label class, while maximizing the minimum pairwise distance. For small-scale cross-group representative selection, we propose the first three-stage framework—pre-pruning, padded decomposition, and label-aware assignment. We introduce a distance-driven pre-pruning step to improve efficiency; employ randomized padded decomposition to balance intra-group sparsity and global diversity; and design a label-aware cluster assignment mechanism to ensure fair label coverage. We theoretically establish an approximation ratio of $Omega(sqrt{log m}/m)$, significantly improving upon prior methods. Experiments on large-scale datasets demonstrate that our approach achieves state-of-the-art performance in both minimum pairwise distance and label coverage, while strictly satisfying fairness constraints.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Search and Optimization: Distributed Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Diversity maximization problem is a well-studied problem where the goal is to find $k$ diverse items. Fair diversity maximization aims to select a diverse subset of $k$ items from a large dataset, while requiring that each group of items be well represented in the output. More formally, given a set of items with labels, our goal is to find $k$ items that maximize the minimum pairwise distance in the set, while maintaining that each label is represented within some budget. In many cases, one is only interested in selecting a handful (say a constant) number of items from each group. In such scenario we show that a randomized algorithm based on padded decompositions improves the state-of-the-art approximation ratio to $sqrt{log(m)}/(3m)$, where $m$ is the number of labels. The algorithms work in several stages: ($i$) a preprocessing pruning which ensures that points with the same label are far away from each other, ($ii$) a decomposition phase, where points are randomly placed in clusters such that there is a feasible solution with maximum one point per cluster and that any feasible solution will be diverse, $(iii)$ assignment phase, where clusters are assigned to labels, and a representative point with the corresponding label is selected from each cluster. We experimentally verify the effectiveness of our algorithm on large datasets.

Problem

• Maximize diversity while ensuring fair group representation
• Select diverse items with label-specific budget constraints
• Improve approximation ratio for few representatives per group

Innovation

• Preprocessing pruning for label distance
• Randomized padded decomposition clustering
• Cluster-label assignment with diversity