Private learning of halfspaces: Simplifying the construction & reducing the sample complexity

Haim Kaplan; Yishay Mansour; Uri Stemmer; Eliad Tsfadia

Private learning of halfspaces: Simplifying the construction & reducing the sample complexity

Haim Kaplan, Yishay Mansour, Uri Stemmer, Eliad Tsfadia

Department of Computer Science

Research output: Contribution to journal › Conference article › peer-review

10 Scopus citations

Abstract

We present a differentially private learner for halfspaces over a finite grid G in R^d with sample complexity ˜ d^2.5 · 2^{log* |}G^|, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a d² factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of m linear constraints of the form Ax = b, the task is to privately identify a solution x that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution x.

Original language	English
Journal	Advances in Neural Information Processing Systems
Volume	2020-December
State	Published - 1 Jan 2020
Event	34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online Duration: 6 Dec 2020 → 12 Dec 2020

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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title = "Private learning of halfspaces: Simplifying the construction & reducing the sample complexity",

abstract = "We present a differentially private learner for halfspaces over a finite grid G in Rd with sample complexity ˜ d2.5 · 2log* |G|, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a d2 factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of m linear constraints of the form Ax = b, the task is to privately identify a solution x that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution x.",

author = "Haim Kaplan and Yishay Mansour and Uri Stemmer and Eliad Tsfadia",

note = "Publisher Copyright: {\textcopyright} 2020 Neural information processing systems foundation. All rights reserved.; 34th Conference on Neural Information Processing Systems, NeurIPS 2020 ; Conference date: 06-12-2020 Through 12-12-2020",

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T2 - 34th Conference on Neural Information Processing Systems, NeurIPS 2020

AU - Kaplan, Haim

AU - Mansour, Yishay

AU - Stemmer, Uri

AU - Tsfadia, Eliad

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We present a differentially private learner for halfspaces over a finite grid G in Rd with sample complexity ˜ d2.5 · 2log* |G|, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a d2 factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of m linear constraints of the form Ax = b, the task is to privately identify a solution x that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution x.

AB - We present a differentially private learner for halfspaces over a finite grid G in Rd with sample complexity ˜ d2.5 · 2log* |G|, which improves the state-of-the-art result of [Beimel et al., COLT 2019] by a d2 factor. The building block for our learner is a new differentially private algorithm for approximately solving the linear feasibility problem: Given a feasible collection of m linear constraints of the form Ax = b, the task is to privately identify a solution x that satisfies most of the constraints. Our algorithm is iterative, where each iteration determines the next coordinate of the constructed solution x.

UR - http://www.scopus.com/inward/record.url?scp=85099076812&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85099076812

SN - 1049-5258

VL - 2020-December

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

Y2 - 6 December 2020 through 12 December 2020

ER -

Private learning of halfspaces: Simplifying the construction & reducing the sample complexity

Abstract

ASJC Scopus subject areas

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