Differentially Private Learning of Geometric Concepts

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Haim Kaplan, Yishay Mansour, Yossi Matias, Uri Stemmer ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:3233-3241, 2019.

Abstract

We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(\alpha,\beta)$-PAC learning and $(\epsilon,\delta)$-differential privacy using a sample of size $\tilde{O}\left(\frac{1}{\alpha\epsilon}k\log d\right)$, where the domain is $[d]\times[d]$ and $k$ is the number of edges in the union of polygons.

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