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On Differentially Private Online Collaborative Recommendation Systems

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Information Security and Cryptology - ICISC 2015 (ICISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9558))

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Abstract

In collaborative recommendation systems, privacy may be compromised, as users’ opinions are used to generate recommendations for others. In this paper, we consider an online collaborative recommendation system, and we measure users’ privacy in terms of the standard notion of differential privacy. We give the first quantitative analysis of the trade-offs between recommendation quality and users’ privacy in such a system by showing a lower bound on the best achievable privacy for any algorithm with non-trivial recommendation quality, and proposing a near-optimal algorithm. From our results, we find that there is actually little trade-off between recommendation quality and privacy, as long as non-trivial recommendation quality is to be guaranteed. Our results also identify the key parameters that determine the best achievable privacy.

A full version [21] of this paper is available at http://arxiv.org/abs/1510.08546. This research was supported by MOE ARC-2 grant MOE2014-T2-1-157.

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Notes

  1. 1.

    Technically, the assumptions that \(n = O(\mathrm {polylog}(T))\), \(P \ge 6m\) and \(R = O(T^\nu )\) are only for showing the near-optimality of our lower bound. Our lower bound itself remains to hold without these assumptions.

  2. 2.

    On the other hand, our privacy definition does not imply their definitions either. Therefore these two types of privacy models are incomparable.

  3. 3.

    This statement actually holds for all the algorithms with o(T) loss. In Theorem 1, we choose \(O(T^\eta )\) target loss to get a clean expression for the lower bound on \(\epsilon \), and a similar (but messier) lower bound on \(\epsilon \) holds for o(T) target loss too.

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Authors and Affiliations

  1. School of Computing, National University of Singapore, Singapore, Singapore

    Seth Gilbert, Xiao Liu & Haifeng Yu

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  1. Seth Gilbert
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  2. Xiao Liu
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Correspondence to Xiao Liu .

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  1. Sungkyunkwan University, Suwon, Gyeonggi, Korea (Republic of)

    Soonhak Kwon

  2. UNIST, Ulsan, Korea (Republic of)

    Aaram Yun

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Gilbert, S., Liu, X., Yu, H. (2016). On Differentially Private Online Collaborative Recommendation Systems. In: Kwon, S., Yun, A. (eds) Information Security and Cryptology - ICISC 2015. ICISC 2015. Lecture Notes in Computer Science(), vol 9558. Springer, Cham. https://doi.org/10.1007/978-3-319-30840-1_14

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