Fair Clustering Through Fairlets (1802.05733v1)

Abstract: We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the $k$-center and the $k$-median objectives, and show that even with two protected classes the problem is challenging, as the optimum solution can violate common conventions---for instance a point may no longer be assigned to its nearest cluster center! En route we introduce the concept of fairlets, which are minimal sets that satisfy fair representation while approximately preserving the clustering objective. We show that any fair clustering problem can be decomposed into first finding good fairlets, and then using existing machinery for traditional clustering algorithms. While finding good fairlets can be NP-hard, we proceed to obtain efficient approximation algorithms based on minimum cost flow. We empirically quantify the value of fair clustering on real-world datasets with sensitive attributes.

Analyzing "Fair Clustering Through Fairlets"

The paper "Fair Clustering Through Fairlets" addresses the problem of fair clustering under the doctrine of disparate impact, emphasizing the necessity for balanced representation of protected classes within each cluster. The authors explore this issue in the context of two common clustering objectives, namely, $k$-center and $k$-median. Their formulations challenge conventional assumptions, illustrating that achieving fairness can alter typical clustering outcomes, such as assigning points to their nearest cluster center.

Key Contributions

The paper introduces the concept of "fairlets," defined as minimal sets that satisfy fair representation while retaining approximate clustering objectives. This concept is pivotal as it enables the decomposition of fair clustering problems into two stages: finding optimal fairlets and then applying standard clustering algorithms. Although identifying optimal fairlets is NP-hard, the authors propose efficient approximation algorithms utilizing minimum cost flow techniques. The paper empirically evaluates the impact of incorporating fairness into clustering on real-world datasets featuring sensitive attributes.

Implications and Empirical Analysis

The approach outlined in the paper involves first partitioning the dataset into fairlets which respect the fairness constraints, and subsequently applying classical clustering methods to the centroids of these fairlets. This two-step methodology ensures that the results respect fair representation constraints across clusters. The algorithms are shown to have solid approximation bounds: The $k$-center and $k$-median problems achieve 4-approximation and a $(2+\sqrt{3}+\epsilon)$-approximation, respectively.

In empirical analyses, the paper demonstrates a trade-off between fairness and clustering cost. Traditional clustering methods often yield solutions that lack balance among protected classes, indicating a significant disparate impact. However, employing fair matching and fairlet decomposition significantly improves balance—albeit at an increased cost—in alignment with the underlying fairness constraints.

Theoretical and Practical Insights

• Theoretical Insights: The introduction of fairlets abstracts the multicoloring requirement of balanced clustering into a simpler representation problem. This abstraction links fairness issues directly to existing mathematical frameworks such as minimum cost flow, facilitating the application of established techniques and enriching the intersection of fairness and combinatorial optimization.
• Practical Implications: The algorithms developed offer a practical pathway for deploying fair clustering in real-world applications where balance across sensitive attributes is critical. This is particularly relevant in domains like finance, healthcare, and criminal justice, where algorithmic decisions carry significant societal consequences.

Directions for Future Research

This work paves the way for further exploration into balancing fairness with computational efficiency and clustering quality. Future research could focus on tightening the bounds of fairlet decomposition algorithms or extending the fairlet concept to non-binary protected class scenarios, which involve additional complexity in defining fairness and proving algorithmic hardness.

Overall, "Fair Clustering Through Fairlets" provides a comprehensive framework for fair clustering, addressing both theoretical challenges and practical necessities. The methodologies and insights could catalyze advancements in fairness-aware machine learning, ensuring more equitable algorithmic decision-making.