Fair and Representative Subset Selection from Data Streams

TL;DR

This paper introduces efficient algorithms for fair subset selection from data streams, ensuring representation across groups while maximizing a submodular function, with applications in graph coverage and recommendations.

Contribution

It proposes the first approximation algorithms for fairness-aware streaming submodular maximization with theoretical guarantees and practical efficiency.

Findings

Achieves a (1/2 - ε)-approximation with multiple passes over data.

Single-pass algorithm with same approximation ratio under unlimited buffer.

Demonstrates effectiveness on graph coverage and personalized recommendation tasks.

Abstract

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be formulated as maximizing a monotone submodular function subject to a cardinality constraint $k$. In this work, we consider the setting where data items in the stream belong to one of several disjoint groups and investigate the optimization problem with an additional \emph{fairness} constraint that limits selection to a given number of items from each group. We then propose efficient algorithms for the fairness-aware variant of the streaming submodular maximization problem. In particular, we first give a $ (\frac{1}{2}-\varepsilon) $-approximation algorithm that requires $ O(\frac{1}{\varepsilon} \log \frac{k}{\varepsilon}) $ passes over the stream for any constant $ \varepsilon>0 $. Moreover, we give a single-pass streaming algorithm that has the same approximation ratio of $(\frac{1}{2}-\varepsilon)$ when unlimited buffer sizes and post-processing time are permitted, and discuss how to adapt it to more practical settings where the buffer sizes are bounded. Finally, we demonstrate the efficiency and effectiveness of our proposed algorithms on two real-world applications, namely \emph{maximum coverage on large graphs} and \emph{personalized recommendation}.