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Fair Clustering: Critique, Caveats, and Future Directions

John Dickerson, Seyed A. Esmaeili, Jamie Morgenstern, Claire Jie Zhang

TL;DR

This paper critiques the fair clustering literature by highlighting missing utility characterizations and potentially harmful downstream welfare effects. It contrasts OR facility-location and ML clustering perspectives, formalizes CM, SF, and EQ notions, and introduces the price of fairness as $PoF = \frac{\text{Cost of Optimal Solution Satisfying Constraint}}{\text{Cost of Optimal Agnostic Solution}}$. Through illustrative examples, it shows that enforcing fairness can increase distances or cause unequal welfare degradation across groups, and it discusses unintended ML pipeline consequences such as outlier detection and per-cluster modeling. It concludes with a path toward more impactful research, advocating welfare-centered formulations, realistic real-world data, long-term analyses, standards, and stakeholder engagement.

Abstract

Clustering is a fundamental problem in machine learning and operations research. Therefore, given the fact that fairness considerations have become of paramount importance in algorithm design, fairness in clustering has received significant attention from the research community. The literature on fair clustering has resulted in a collection of interesting fairness notions and elaborate algorithms. In this paper, we take a critical view of fair clustering, identifying a collection of ignored issues such as the lack of a clear utility characterization and the difficulty in accounting for the downstream effects of a fair clustering algorithm in machine learning settings. In some cases, we demonstrate examples where the application of a fair clustering algorithm can have significant negative impacts on social welfare. We end by identifying a collection of steps that would lead towards more impactful research in fair clustering.

Fair Clustering: Critique, Caveats, and Future Directions

TL;DR

This paper critiques the fair clustering literature by highlighting missing utility characterizations and potentially harmful downstream welfare effects. It contrasts OR facility-location and ML clustering perspectives, formalizes CM, SF, and EQ notions, and introduces the price of fairness as . Through illustrative examples, it shows that enforcing fairness can increase distances or cause unequal welfare degradation across groups, and it discusses unintended ML pipeline consequences such as outlier detection and per-cluster modeling. It concludes with a path toward more impactful research, advocating welfare-centered formulations, realistic real-world data, long-term analyses, standards, and stakeholder engagement.

Abstract

Clustering is a fundamental problem in machine learning and operations research. Therefore, given the fact that fairness considerations have become of paramount importance in algorithm design, fairness in clustering has received significant attention from the research community. The literature on fair clustering has resulted in a collection of interesting fairness notions and elaborate algorithms. In this paper, we take a critical view of fair clustering, identifying a collection of ignored issues such as the lack of a clear utility characterization and the difficulty in accounting for the downstream effects of a fair clustering algorithm in machine learning settings. In some cases, we demonstrate examples where the application of a fair clustering algorithm can have significant negative impacts on social welfare. We end by identifying a collection of steps that would lead towards more impactful research in fair clustering.
Paper Structure (36 sections, 1 theorem, 19 equations, 8 figures)

This paper contains 36 sections, 1 theorem, 19 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Contributions and Organization of the Paper.
  3. Review of Clustering and Fair Clustering
  4. Two Perspectives in Clustering: Operations Research vs Machine Learning
  5. Operations Research (OR):
  6. Machine Learning (ML):
  7. Brief Review of Fair Clustering
  8. Proportional Color Mixing (CM):
  9. Socially Fair Clustering (SF):
  10. Equitable Distance Fairness (EQ):
  11. How Does Fair Clustering Affect Utility and Welfare?
  12. Fair Clustering Could Degrade Welfare
  13. CM Constraint Example.
  14. EQ Constraint Example.
  15. SF Constraint Example.
  16. ...and 21 more sections

Key Result

Theorem 3.1

In the instance shown in Figure fig:welfare_example, for the $k$-median problem with $k=4$ a CM or an SF clustering would have an average utility of at most $2r$ for each group whereas a welfare-centric clustering would result in an average utility of at least $3 r$ where $r$ is a positive number.

Figures (8)

  • Figure 1: The figure shows an instance with the agnostic vs the CM clustering output. Note that centers are labeled by a green marker X.
  • Figure 2: The figure shows an instance with the agnostic vs the EQ clustering output. Note that centers are labeled by a green marker X..
  • Figure 3: The figure shows an instance with the agnostic vs the SF clustering output. Note that centers are labelled by a green marker X.
  • Figure 4: In this example points which are nearby points (the four triads and the four blue point middle points) are separated by a small distance of $\epsilon$ whereas every other distance between any two points is at least $R \gg \epsilon$. Although the two CM clustering solutions in the bottom row have approximately equal clustering cost they result in different distance assignments for the red and blue groups. The first is favorable to the blue group wherease the second is favorable to the red group.
  • Figure 5: The figure shows the input instance consisting of two regions $R_1$ and $R_2$ separated by a very large distance $D$ ($D$ is shown smaller in the figure to save space). The resulting clusterings for CM, SF, and the welfare-centric WC clusterings are all shown with the clusters enclosed by dashed lines and centers with green X. Note how WC gives the most natural solution which is a mixture of both CM and SF, achieving diversity only when it comes at a reasonable expense.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Theorem 3.1
  • proof