Distributional Individual Fairness in Clustering
This addresses fairness in clustering for applications like data analysis and resource allocation, offering a novel approach beyond group fairness, though it builds on existing individual fairness concepts from classification.
The paper tackles fair clustering by introducing individual fairness, ensuring similar individuals are assigned to statistically similar distributions over clusters, and provides an algorithm with provable approximation guarantees for p-norm objectives like k-center and k-means.
In this paper, we initiate the study of fair clustering that ensures distributional similarity among similar individuals. In response to improving fairness in machine learning, recent papers have investigated fairness in clustering algorithms and have focused on the paradigm of statistical parity/group fairness. These efforts attempt to minimize bias against some protected groups in the population. However, to the best of our knowledge, the alternative viewpoint of individual fairness, introduced by Dwork et al. (ITCS 2012) in the context of classification, has not been considered for clustering so far. Similar to Dwork et al., we adopt the individual fairness notion which mandates that similar individuals should be treated similarly for clustering problems. We use the notion of $f$-divergence as a measure of statistical similarity that significantly generalizes the ones used by Dwork et al. We introduce a framework for assigning individuals, embedded in a metric space, to probability distributions over a bounded number of cluster centers. The objective is to ensure (a) low cost of clustering in expectation and (b) individuals that are close to each other in a given fairness space are mapped to statistically similar distributions. We provide an algorithm for clustering with $p$-norm objective ($k$-center, $k$-means are special cases) and individual fairness constraints with provable approximation guarantee. We extend this framework to include both group fairness and individual fairness inside the protected groups. Finally, we observe conditions under which individual fairness implies group fairness. We present extensive experimental evidence that justifies the effectiveness of our approach.