Scalable Differentially Private Clustering via Hierarchically Separated Trees

• URL: http://arxiv.org/abs/2206.08646v1
• Date: Fri, 17 Jun 2022 09:24:41 GMT
• Title: Scalable Differentially Private Clustering via Hierarchically Separated Trees
• Authors: Vincent Cohen-Addad, Alessandro Epasto, Silvio Lattanzi, Vahab Mirrokni, Andres Munoz, David Saulpic, Chris Schwiegelshohn, Sergei Vassilvitskii
• Abstract summary: We show that our method computes a solution with cost at most $O(d3/2log n)cdot OPT + O(k d2 log2 n / epsilon2)$, where $epsilon$ is the privacy guarantee. Although the worst-case guarantee is worse than that of state of the art private clustering methods, the algorithm we propose is practical.
• Score: 82.69664595378869
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most $O(d^{3/2}\log n)\cdot OPT + O(k d^2 \log^2 n / \epsilon^2)$, where $\epsilon$ is the privacy guarantee. (The dimension term, $d$, can be replaced with $O(\log k)$ using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of the art private clustering methods, the algorithm we propose is practical, runs in near-linear, $\tilde{O}(nkd)$, time and scales to tens of millions of points. We also show that our method is amenable to parallelization in large-scale distributed computing environments. In particular we show that our private algorithms can be implemented in logarithmic number of MPC rounds in the sublinear memory regime. Finally, we complement our theoretical analysis with an empirical evaluation demonstrating the algorithm's efficiency and accuracy in comparison to other privacy clustering baselines.

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