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Differentially Private Learning of Geometric Concepts

Haim Kaplan
Yishay Mansour
Siam J. on Computing (2022)

Abstract

We present differentially private efficient algorithms for learning polygons in the plane (which are not necessarily convex). Our algorithm achieves $(\alpha,\beta)$-PAC learning and $(\eps,\delta)$-differential privacy using a sample of size $O\left(\frac{k}{\alpha\eps}\log\left(\frac{|X|}{\beta\delta}\right)\right)$, where the domain is $X\times X$ and $k$ is the number of edges in the (potentially non-convex) polygon.