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The price of privacy and the limits of LP decoding

Published: 11 June 2007 Publication History

Abstract

This work is at theintersection of two lines of research. One line, initiated by Dinurand Nissim, investigates the price, in accuracy, of protecting privacy in a statistical database. The second, growing from an extensive literature on compressed sensing (see in particular the work of Donoho and collaborators [4,7,13,11])and explicitly connected to error-correcting codes by Candès and Tao ([4]; see also [5,3]), is in the use of linearprogramming for error correction.
Our principal result is the discovery of a sharp threshhold ρ*∠ 0.239, so that if ρ < ρ* and A is a random m x n encoding matrix of independently chosen standardGaussians, where m = O(n), then with overwhelming probability overchoice of A, for all x ∈ Rn, LP decoding corrects ⌊ ρ m⌋ arbitrary errors in the encoding Ax, while decoding can be made to fail if the error rate exceeds ρ*. Our boundresolves an open question of Candès, Rudelson, Tao, and Vershyin [3] and (oddly, but explicably) refutesempirical conclusions of Donoho [11] and Candès et al [3]. By scaling and rounding we can easilytransform these results to obtain polynomial-time decodable random linear codes with polynomial-sized alphabets tolerating any ρ < ρ* ∠ 0.239 fraction of arbitrary errors.
In the context of privacy-preserving datamining our results say thatany privacy mechanism, interactive or non-interactive, providingreasonably accurate answers to a 0.761 fraction of randomly generated weighted subset sum queries, and arbitrary answers on the remaining 0.239 fraction, is blatantly non-private.

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cover image ACM Conferences
STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
June 2007
734 pages
ISBN:9781595936318
DOI:10.1145/1250790
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Published: 11 June 2007

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Author Tags

  1. LP decoding
  2. basis pursuit
  3. compressed sensing
  4. privacy

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June 11 - 13, 2007
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  • (2024)QueryCheetah: Fast Automated Discovery of Attribute Inference Attacks Against Query-Based SystemsProceedings of the 2024 on ACM SIGSAC Conference on Computer and Communications Security10.1145/3658644.3690272(3451-3465)Online publication date: 2-Dec-2024
  • (2024)Anonymization: The imperfect science of using data while preserving privacyScience Advances10.1126/sciadv.adn705310:29Online publication date: 19-Jul-2024
  • (2024)Probabilistic Dataset Reconstruction from Interpretable Models2024 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML)10.1109/SaTML59370.2024.00009(1-17)Online publication date: 9-Apr-2024
  • (2023)Multi-task differential privacy under distribution skewProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619139(17784-17807)Online publication date: 23-Jul-2023
  • (2023)Exploiting Fairness to Enhance Sensitive Attributes Reconstruction2023 IEEE Conference on Secure and Trustworthy Machine Learning (SaTML)10.1109/SaTML54575.2023.00012(18-41)Online publication date: Feb-2023
  • (2023)Towards Separating Computational and Statistical Differential Privacy2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00042(580-599)Online publication date: 6-Nov-2023
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  • (2022)Reconstructing Training Data with Informed Adversaries2022 IEEE Symposium on Security and Privacy (SP)10.1109/SP46214.2022.9833677(1138-1156)Online publication date: May-2022
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