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Poster
Optimal Private Median Estimation under Minimal Distributional Assumptions
Christos Tzamos · Emmanouil-Vasileios Vlatakis-Gkaragkounis · Ilias Zadik

Tue Dec 08 09:00 AM -- 11:00 AM (PST) @ Poster Session 1 #264

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a positive density at a small neighborhood around the median. In particular, the distribution is allowed to output unbounded values and is not required to have finite moments. We compute the exact, up-to-constant terms, statistical rate of estimation for the median by providing nearly-tight upper and lower bounds. Furthermore, we design a polynomial-time differentially private algorithm which provably achieves the optimal performance. At a technical level, our results leverage a Lipschitz Extension Lemma which allows us to design and analyze differentially private algorithms solely on appropriately defined ``typical" instances of the samples.

Author Information

Christos Tzamos (UW-Madison)
Emmanouil-Vasileios Vlatakis-Gkaragkounis (Columbia University)
Ilias Zadik (NYU)

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