Probabilistic Fair Clustering
This work addresses fair clustering for scenarios with uncertain group membership, which is an incremental extension of prior deterministic methods.
The paper tackles the problem of fair clustering when group membership is known only probabilistically, rather than deterministically, and presents algorithms with approximation ratio guarantees for this setting, including experiments that validate the approach and highlight nuanced concerns.
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color (e.g., membership in a group), and the features of a valid clustering might also include the representation of colors in that clustering. Prior work in fair clustering assumes complete knowledge of group membership. In this paper, we generalize prior work by assuming imperfect knowledge of group membership through probabilistic assignments. We present clustering algorithms in this more general setting with approximation ratio guarantees. We also address the problem of "metric membership", where different groups have a notion of order and distance. Experiments are conducted using our proposed algorithms as well as baselines to validate our approach and also surface nuanced concerns when group membership is not known deterministically.