Differentially Private Algorithms for Clustering with Stability Assumptions
Abstract
We study the problem of differentially private clustering under input-stability assumptions. Despite the ever-growing volume of works on differential privacy in general and differentially private clustering in particular, only three works (Nissim et al. 2007, Wang et al. 2015, Huang et al. 2018) looked at the problem of privately clustering "nice" k-means instances, all three relying on the sample-and-aggregate framework and all three measuring utility in terms of Wasserstein distance between the true cluster centers and the centers returned by the private algorithm. In this work we improve upon this line of works on multiple axes. We present a far simpler algorithm for clustering stable inputs (not relying on the sample-and-aggregate framework), and analyze its utility in both the Wasserstein distance and the k-means cost. Moreover, our algorithm has straight-forward analogues for "nice" k-median instances and for the local-model of differential privacy.
Cite
@article{arxiv.2106.12959,
title = {Differentially Private Algorithms for Clustering with Stability Assumptions},
author = {Moshe Shechner},
journal= {arXiv preprint arXiv:2106.12959},
year = {2021}
}
Comments
Thesis submitted in partial fulfillment of the requirements for the M. Sc. degree in the Faculty of Natural Sciences. arXiv admin note: text overlap with arXiv:1907.02513 by other authors