DIFFERENTIALLY PRIVATE LEARNING OF GEOMETRIC CONCEPTS

Haim Kaplan; Yishay Mansour; Yossi Matias; Uri Stemmer

doi:10.1137/21M1427450

DIFFERENTIALLY PRIVATE LEARNING OF GEOMETRIC CONCEPTS

Haim Kaplan, Yishay Mansour, Yossi Matias, Uri Stemmer

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	952-974
Number of pages	23
Journal	SIAM Journal on Optimization
Volume	32
Issue number	3
DOIs	https://doi.org/10.1137/21M1427450
State	Published - 1 Jan 2022
Externally published	Yes

Keywords

PAC learning
differential privacy
polygons

ASJC Scopus subject areas

Software
Theoretical Computer Science
Applied Mathematics

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10.1137/21M1427450

Cite this

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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",

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PY - 2022/1/1

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N2 - 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.

AB - 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.

KW - PAC learning

KW - differential privacy

KW - polygons

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DIFFERENTIALLY PRIVATE LEARNING OF GEOMETRIC CONCEPTS

Abstract

Keywords

ASJC Scopus subject areas

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