Title: Individually Fair Diversity Maximization
Venue: NeurIPS 2025
Accepted: yes
Keywords: fairness

diversity maximization
Abstract: We consider the problem of diversity maximization from the perspective of individual fairness: given a set $P$ of $n$ points in a metric space, we aim to extract a subset $S$ of size $k$ from $P$ so that (1) the diversity of $S$ is maximized and (2) $S$ is \emph{individually fair} in the sense that every point in $P$ has at least one of its $\frac{n}{k}$-nearest neighbors as its ``representative'' in $S$. We propose $\left(O(1), 3\right)$-bicriteria approximation algorithms for the individually fair variants of the three most common diversity maximization problems, namely, max-min diversification, max-sum diversification, and sum-min diversification. Specifically, the proposed algorithms provide a set of points where every point in the dataset finds a point within a distance at most $3$ times its distance to its $\frac{n}{k}$-nearest neighbor while achieving a diversity value at most $O(1)$ times lower than the optimal solution. Numerical experiments on real-world and synthetic datasets demonstrate that the proposed algorithms generate solutions that are individually fairer than those produced by unconstrained algorithms and incur only modest losses in diversity.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper discusses the problem of finding a diverse set of k points from a given point set in a metric space. There are three ways of quantifying diversity:\n1. max-min diversification: maximize the minimum distance between any pair of selected points,\n2. max-sum diversification: maximize the sum of pairwise distances between selected points, and \n3. sum-min diversification: maximize the sum of the minimum distances from each selected point to its nearest neighbor among the other selected points. \n\nThese problems are well-studied in the literature, and an approximation lower bound of 2 is known for them. Approximation algorithms closely matching the lower bound are also known. This paper explores these problems with an additional constraint that every point in the point set has at least one of its (n/k)-nearest neighbors as its “representative” among the chosen k points. This property is called the individually fair property.\n\nThe paper gives approximation algorithms for the three diversity problem with the added individually fair constraint. The nature of the approximation algorithm is a bicriteria (a, b) approximation, where a is the approximation guarantee for the diversity objective, and b is the factor by which the individually fair radius is exceeded. \n\nThe algorithm uses the following reduction-based idea:\n- First, the set of points is partitioned into (approximate) individually fair regions.\n- Then, a known approximation algorithm for the diversity problem under the partition matroid is used on the point set and the partition to obtain the bicriteria approximation algorithm.\n\nExperiments are performed and observations are made about the algorithms with and without the individually fair constraint.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Theoretical results about two opposing objectives (diversity and individual fairness) are good to know. The problem formulation makes sense and may be useful.\n\n\nWeaknesses:\n- Since the major part of this work is theoretical, the lack of approximation lower bound statements to support some of the approximation upper bounds stands out and can be seen as a weakness.\n- Discussions related to checking whether there is a feasible solution for the individually fair problem seem to be missing. It'll be good to have this discussion.\n- The experimental results are designed to observe properties of the problem and the suggested algorithm. Some experiments that can motivate the problem formulation can help to make the paper more interesting.\n\nQUESTIONS:\nComments: \n- (lines 61 - 75): Bicriteria approximation has not been defined in the paper yet. It is only defined later. So, it is difficult to read. Also, what purpose does \\alpha serve in these statements?\n- Other questions are mentioned in the summary and strengths and weaknesses.\n\nLIMITATIONS:\nYes. The paper presents theoretical results that do not have any potential negative societal impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies a combination of diversity maximization and individual fairness in centroid clustering. Diversity maximization requires that the selected points are (in some sense) sufficiently spread out, while individual fairness requires that every point in the clustering instance should have a selected center somewhere in their vicinity. The paper gives a general framework for approximating diversity subject to approximate individual fairness. This framework guarantees bi-criteria approximations to both.\n\nSTRENGTHS AND WEAKNESSES:\nIn general this seems like a solid paper. Both diversity maximization and individual fairness are problems that are somewhat frequently studied, and combining them seems natural. There is a lot of work on bi-criteria optimization for standard clustering objectives (such as k-center or k-means), so why not design bi-criteria optimization algorithms for diversity maximization. In its techniques the paper is very similar to those previous works (which is not really surprising as for instance k-center and Max-Min Diversification are closely related, with the tight $2$-approximations for either essentially being the same algorithm). For instance, the construction of the individual fairness regions here is essentially the same as what is done in ``A Subquadratic Time Approximation Algorithm for Individually\nFair k-Center'' by Ebbens et al. at AISTATS this year (I briefly thought that one might be able to directly apply their algorithm here as well, but this is not as easy, as the algorithm of Ebbens et al. can select strictly less than $k$ points and filling after these points is crucial) and I think a bit more discussion on why previous algorithms fail would have been nice.\n\nIn general, while I think that the paper is solid, I am not entirely sure if it is strong enough for NeurIPS. In particular, the paper does not feel very significant to me, and more like another twist on an already mostly established formula. I am willing to be convinced by the other reviewers here, though.\n\nMinor Comments:\n- Line 50: \"an individual notion of fairness\" reads a bit weird to me\n- Line 50-51: You should probably note that such a clustering does not always exist\n- Line 54: How does this example related to clustering? While this is a \"subset-selection\" problem it is not really a clustering problem. Also I am not really sure you want your measures of diversity in such a setting.\n- Our Contributions: \\alpha is undefined here\n- Line 109: Technically the group fairness notion studied by paper [10] is the nearly equivalent to individual fairness as studied in this paper, see \"Proportional fairness in clustering: A social choice perspective\", Kellerhals and Peters, NeurIPS 2024\n- \"seminal work\" might be too high praise\n- Line 123: \\mapsto should be \\to\n- Line 125: \"to denote the subset of points.\" what do you mean by \"the subset of points\"?\n- Line 131 onwards: You do not really need P in the definitions, also missing {} around the u(s)\n- Line 152: You should briefly mention that alpha = 2 can be achieved and that this is tight.\n- I found the statements of Theorems 1, 2,3 to be somewhat unclean, maybe they could be written nicer.\n- Line 531: Mathmode around n/k missing\n\nQUESTIONS:\nNone currently\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper focused on the diversity maximization problem with the additional constraint of individual fairness based neighborhood radii as introduced in Jung et al. Three diversity maximization objectives are considered (max-min, max-sum, sum-min) and approximation bicriteria algorithms with guarantees are introduced for them.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n-The paper is mostly well-written.\n\n-I did not have a chance to look at the proofs, but the derivations do not seem trivial. \n\n## Weaknesses\n\nI think the major issues are with the motivation for the model/notion of fairness and the parameter $m$ and the runtime in Theorem 4. More details:\n\n1-The motivation of the problem is not clear. Why is this notion of fairness needed? The objectives (1-3) on page 3 are all calculated based on S, but definition 2 on page 4 is based on all of the Points in P not in S? The paper does not give any motivations for the model.  \n\n2-lines (52-57), I don’t see how the corporate recruitment example is a good motivation for additionally imposing the n/k constraint? How does it guarantee that every qualified applicant has a chance of being interviewed?\n\n3-There is an issue with Theorem 4. In particular, the run-time is exponential in k which is a big disadvantage. Further, I cannot understand the bound on the value of $m$ , is it not the case that $m \\leq k$ . This would make the result significantly weaker. If the run-time can indeed be very slow in terms of k, then I think the paper should've been clear about this. Especially, since the other objectives do not have a similar problem. \n\n4-Is the experimental section comparing against any baselines? I don’t see where the baselines are?\n\n\nMinor Points:\n\n1-‘Non-private’ line 13, replace by something like unfair instead.\n\n2-In definition 3 on page 4, for point 2. It should be just $\\gamma$ not $\\gamma \\dot \\alpha$, correct?\n\n3-What is the GMM algorithm in line 323?\n\nQUESTIONS:\nPlease see weaknesses above.\n\nLIMITATIONS:\nNo real need to discuss potential negative societal impact.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this paper, the authors study the problem of diversity maximization under individual fairness constraints. The objective is to select a subset of $k$ points from a dataset such that diversity is maximized while ensuring fairness, where every point has a representative within a bounded distance. The authors provide a $(O(1), 3)$ bicriteria approximation algorithm, where the representative is at most $3$ times the distance to the nearest neighbor, and diversity is a constant fraction of the optimal diversity. These algorithms leverage fairness-aware partitioning techniques and matroid-based optimization to achieve theoretical guarantees for fairness and diversity. Empirical evaluations on real-world and synthetic datasets validate their approach.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**:\n\nWhile group fairness has been well studied, individual fairness with diversity-based objectives has not been studied before. The motivation of the setting is novel and an important addition to the diversity maximization literature. The authors provide approximation algorithmic results for different diversity maximization objectives studied in the literature with individual fairness.\n\nMany prior works (on group fairness) design algorithms by reduction to partition matroids. In this work, the authors design an interesting approach of partitioning the points into individual fairness regions and then employing partition matroid methods to satisfy the constraints.\n\n**Weaknesses**:\n\nThe algorithmic novelty is limited. It would be interesting to see if there is a way to improve on the $O(1)$ guarantees. It suggests that the guarantee is because of the partition matroid, and it is not immediately clear how hard the problem is with respect to group fairness.\n\nThe computational complexity of $O(n^2)$ is certainly a challenge when scaling up to real-world datasets. It would be interesting to understand if there is a hardness result (fine-grained complexity) with regard to computational complexity.\n\nQUESTIONS:\nCan the authors comment on whether diversity maximization with individual fairness constraints versus group fairness constraints is equivalent in terms of computational hardness? Or is there any reduction between these problems?\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}