Corpus ID: 221150459

Differentially Private Clustering: Tight Approximation Ratios

@article{Ghazi2020DifferentiallyPC,
  title={Differentially Private Clustering: Tight Approximation Ratios},
  author={Badih Ghazi and Ravi Kumar and Pasin Manurangsi},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.08007}
}
We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially the same approximation ratios as those that can be obtained by any non-private algorithm, while incurring only small additive errors. This improves upon existing efficient algorithms that only achieve some large constant approximation factors. Our results… Expand
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References

SHOWING 1-10 OF 124 REFERENCES
Differentially Private k-Means with Constant Multiplicative Error
TLDR
This work designs new differentially private algorithms for the Euclidean k-means problem, both in the centralized model and in the local model of differential privacy, achieving significantly improved error guarantees than the previous state-of-the-art. Expand
Optimal Differentially Private Algorithms for k-Means Clustering
TLDR
It is proved a matching lower bound that no (ε, δ)-differentially private algorithm can guarantee Wasserstein distance less than Ømega (Φ2) and, thus, the positive result is optimal up to a constant factor. Expand
Differentially Private Clustering in High-Dimensional Euclidean Spaces
TLDR
This work gives differentially private and efficient algorithms achieving strong guarantees for k-means and k-median clustering when d = Ω(polylog(n), advancing the state-of-the-art result of √ dOPT+ poly(log n, d, k). Expand
Tight Lower Bounds for Differentially Private Selection
  • T. Steinke, Jonathan Ullman
  • Computer Science, Mathematics
  • 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
TLDR
The fingerprinting method is used to provide tight lower bounds for answering an entire set of d queries, but often only some much smaller set of k queries are relevant and the extension allows us to prove lower bounds that depend on both the number of relevant queries and the total number of queries. Expand
Differentially Private K-Means Clustering
TLDR
An improvement of DPLloyd is proposed which is a differentially private version of the Lloyd algorithm and a non-interactive approach EUGkM which publishes aDifferentially private synopsis for k-means clustering is proposed. Expand
Tight Lower Bounds for Locally Differentially Private Selection
TLDR
A tight lower bound is proved on the sample complexity of any non-interactive local differentially private protocol for optimizing a linear function over the simplex and reveals that any local protocol for these problems has exponentially worse dependence on the dimension than corresponding algorithms in the central model. Expand
Approximating k-median via pseudo-approximation
We present a novel approximation algorithm for k-median that achieves an approximation guarantee of 1+√3+ε, improving upon the decade-old ratio of 3+ε. Our approach is based on two components, eachExpand
Locally Private k-Means Clustering
TLDR
A new algorithm for the Euclidean $k$-means problem that operates in the local model of differential privacy that significantly reduces the additive error while keeping the multiplicative error the same as in previous state-of-the-art results. Expand
Efficient Private Algorithms for Learning Large-Margin Halfspaces
TLDR
These algorithms are based on either differentially private simulations of the statistical query model or on private convex optimization, but the sample complexity of the algorithms depends only on the margin of the data, and not on the dimension. Expand
Approximate clustering via core-sets
TLDR
It is shown that for several clustering problems one can extract a small set of points, so that using those core-sets enable us to perform approximate clustering efficiently and are a substantial improvement over what was previously known. Expand
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