Years and Authors of Summarized Original Work
2014; Nikolov, Talwar, Zhang
2015; Dwork, Nikolov, Talwar
Problem Definition
The central problem of private data analysis is to extract meaningful information from a statistical database without revealing too much about any particular individual represented in the database. Here, by a statistical database, we mean a multiset \(D \in \mathcal{X}^{n}\) of n rows from the data universe\(\mathcal{X}\). The notation \(\vert D\vert \triangleq n\) denotes the size of the database. Each row represents the information belonging to a single individual. The universe \(\mathcal{X}\) depends on the domain. A natural example to keep in mind is \(\mathcal{X} =\{ 0,1\}^{d}\), i.e., each row of the database gives the values of d binary attributes for some individual.
Differential privacy formalizes the notion that an adversary should not learn too much about any individual as a result of a private computation. The formal definition follows.
Definition 1 ([8])...
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Arora S, Hazan E, Kale S (2012) The multiplicative weights update method: a meta-algorithm and applications. Theory Comput 8(1):121–164
Bhaskara A, Dadush D, Krishnaswamy R, Talwar K (2012) Unconditional differentially private mechanisms for linear queries. In: Proceedings of the 44th symposium on theory of computing (STOC’12), New York. ACM, New York, pp 1269–1284. DOI10.1145/2213977.2214089, http://doi.acm.org/10.1145/2213977.2214089
Blum A, Ligett K, Roth A (2008) A learning theory approach to non-interactive database privacy. In: Proceedings of the 40th annual ACM symposium on theory of computing (STOC’08), Victoria. ACM, New York, pp 609–618. http://doi.acm.org/10.1145/1374376.1374464
Bourgain J, Tzafriri L (1987) Invertibility of large submatrices with applications to the geometry of banach spaces and harmonic analysis. Isr J Math 57(2):137–224
Bun M, Ullman J, Vadhan S (2013) Fingerprinting codes and the price of approximate differential privacy. arXiv preprint arXiv:13113158
Dinur I, Nissim K (2003) Revealing information while preserving privacy. In: Proceedings of the 22nd ACM symposium on principles of database systems, San Diego, pp 202–210
Dwork C, Nissim K (2004) Privacy-preserving datamining on vertically partitioned databases. In: Advances in cryptology – CRYPTO’04, Santa Barbara, pp 528–544
Dwork C, Mcsherry F, Nissim K, Smith A (2006) Calibrating noise to sensitivity in private data analysis. In: TCC, New York. http://www.cs.bgu.ac.il/\~kobbi/papers/sensitivity-tcc-final.pdf
Dwork C, McSherry F, Talwar K (2007) The price of privacy and the limits of LP decoding. In: Proceedings of the thirty-ninth annual ACM symposium on theory of computing (STOC’07), San Diego. ACM, New York, pp 85–94. DOI10.1145/1250790.1250804, http://doi.acm.org/10.1145/1250790.1250804
Gupta A, Roth A, Ullman J (2012) Iterative constructions and private data release. In: TCC, Taormina, pp 339–356. http://dx.doi.org/10.1007/978-3-642-28914-9_19
Hardt M, Rothblum G (2010) A multiplicative weights mechanism for privacy-preserving data analysis. In: Proceedings of the 51st foundations of computer science (FOCS), Las Vegas. IEEE
Hardt M, Talwar K (2010) On the geometry of differential privacy. In: Proceedings of the 42nd ACM symposium on theory of computing (STOC’10), Cambridge. ACM, New York, pp 705–714. DOI10.1145/1806689.1806786, http://doi.acm.org/10.1145/1806689.1806786
Li C, Hay M, Rastogi V, Miklau G, McGregor A (2010) Optimizing linear counting queries under differential privacy. In: Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems (PODS’10), Indianapolis. ACM, New York, pp 123–134. http://doi.acm.org/10.1145/1807085.1807104
Lovász L, Spencer J, Vesztergombi K (1986) Discrepancy of set-systems and matrices. Eur J Comb 7(2):151–160
Muthukrishnan S, Nikolov A (2012) Optimal private halfspace counting via discrepancy. In: Proceedings of the 44th symposium on theory of computing (STOC’12), New York. ACM, New York, pp 1285–1292. DOI10.1145/2213977.2214090, http://doi.acm.org/10.1145/2213977.2214090
Nikolov A, Talwar K, Zhang L (2013) The geometry of differential privacy: the sparse and approximate cases. In: Proceedings of the 45th annual ACM symposium on symposium on theory of computing (STOC’13), Palo Alto. ACM, New York, pp 351–360. DOI10.1145/2488608.2488652, http://doi.acm.org/10.1145/2488608.2488652
Plotkin SA, Shmoys DB, Tardos E (1995) Fast approximation algorithms for fractional packing and covering problems. Math Oper Res 20(2):257–301. DOI10.1287/moor.20.2.257, http://dx.doi.org/10.1287/moor.20.2.257
Vershynin R (2001) John’s decompositions: selecting a large part. Isr J Math 122(1):253–277
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Nikolov, A. (2016). Geometric Approaches to Answering Queries. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_553
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