Differentially-Private Hierarchical Clustering with Provable Approximation Guarantees. (arXiv:2302.00037v1 [cs.LG])

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 …

algorithm algorithms applications clustering error framework history input machine machine learning popular private problem study under