Proportional Fairness in Non-Centroid Clustering
Why this work is in the frame
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Bibliographic record
Abstract
We revisit the recently developed framework of proportionally fair clustering, where the goal is to provide group fairness guarantees that become stronger for groups of data points (agents) that are large and cohesive. Prior work applies this framework to centroid clustering, where the loss of an agent is its distance to the centroid assigned to its cluster. We expand the framework to non-centroid clustering, where the loss of an agent is a function of the other agents in its cluster, by adapting two proportional fairness criteria -- the core and its relaxation, fully justified representation (FJR) -- to this setting. We show that the core can be approximated only under structured loss functions, and even then, the best approximation we are able to establish, using an adaptation of the GreedyCapture algorithm developed for centroid clustering [Chen et al., 2019; Micha and Shah, 2020], is unappealing for a natural loss function. In contrast, we design a new (inefficient) algorithm, GreedyCohesiveClustering, which achieves the relaxation FJR exactly under arbitrary loss functions, and show that the efficient GreedyCapture algorithm achieves a constant approximation of FJR. We also design an efficient auditing algorithm, which estimates the FJR approximation of any given clustering solution up to a constant factor. Our experiments on real data suggest that traditional clustering algorithms are highly unfair, whereas GreedyCapture is considerably fairer and incurs only a modest loss in common clustering objectives.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it