@article{4dcd500b5e914f9c9007df1e3f54d272,
title = "DIFFERENTIALLY PRIVATE LEARNING OF GEOMETRIC CONCEPTS",
abstract = "We present efficient differentially private algorithms for learning unions of polygons in the plane (which are not necessarily convex). Our algorithms are (α , β)-probably approximately correct and (ϵ , δ )-differentially private using a sample of size O ( 1 α) , where the domain is [d] × [d] and k is the number of edges in the union of polygons. Our algorithms are obtained by designing a private variant of the classical (nonprivate) learner for conjunctions using the greedy algorithm for set cover.",
keywords = "PAC learning, differential privacy, polygons",
author = "Haim Kaplan and Yishay Mansour and Yossi Matias and Uri Stemmer",
note = "Funding Information: \ast Received by the editors June 22, 2021; accepted for publication (in revised form) February 18, 2022; published electronically July 21, 2022. https://doi.org/10.1137/21M1427450 Funding: This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at LUNARC, partially funded by the Swedish Research Council through grant agreement 2018-05973. \dagger Centre for Mathematical Sciences, Lund University, 221 00 Lund, Sweden (monika.eisenmann@ math.lth.se, tony.stillfjord@math.lth.se). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
month = jan,
day = "1",
doi = "10.1137/21M1427450",
language = "English",
volume = "32",
pages = "952--974",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}