Differentially Private Hierarchical Clustering with Provable Approximation Guarantees

Jacob Imola, Alessandro Epasto, Mohammad Mahdian, Vincent Cohen-Addad, Vahab Mirrokni
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:14353-14375, 2023.

Abstract

Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially-private approximation algorithms for hierarchical clustering under the rigorous framework introduced by Dasgupta (2016). We show strong lower bounds for the problem: that any $\epsilon$-DP algorithm must exhibit $O(|V|^2/ \epsilon)$-additive error for an input dataset $V$. Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2.5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-imola23a, title = {Differentially Private Hierarchical Clustering with Provable Approximation Guarantees}, author = {Imola, Jacob and Epasto, Alessandro and Mahdian, Mohammad and Cohen-Addad, Vincent and Mirrokni, Vahab}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {14353--14375}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/imola23a/imola23a.pdf}, url = {https://proceedings.mlr.press/v202/imola23a.html}, abstract = {Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially-private approximation algorithms for hierarchical clustering under the rigorous framework introduced by Dasgupta (2016). We show strong lower bounds for the problem: that any $\epsilon$-DP algorithm must exhibit $O(|V|^2/ \epsilon)$-additive error for an input dataset $V$. Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2.5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.} }
Endnote
%0 Conference Paper %T Differentially Private Hierarchical Clustering with Provable Approximation Guarantees %A Jacob Imola %A Alessandro Epasto %A Mohammad Mahdian %A Vincent Cohen-Addad %A Vahab Mirrokni %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-imola23a %I PMLR %P 14353--14375 %U https://proceedings.mlr.press/v202/imola23a.html %V 202 %X Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially-private approximation algorithms for hierarchical clustering under the rigorous framework introduced by Dasgupta (2016). We show strong lower bounds for the problem: that any $\epsilon$-DP algorithm must exhibit $O(|V|^2/ \epsilon)$-additive error for an input dataset $V$. Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2.5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private $1+o(1)$ approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.
APA
Imola, J., Epasto, A., Mahdian, M., Cohen-Addad, V. & Mirrokni, V.. (2023). Differentially Private Hierarchical Clustering with Provable Approximation Guarantees. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:14353-14375 Available from https://proceedings.mlr.press/v202/imola23a.html.

Related Material