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## Differential privacy and robust statistics (2009)

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Venue: | STOC'09 |

Citations: | 87 - 2 self |

### Citations

2904 | Robust statistics - Huber - 1981 |

931 |
Robust statistics: the approach based on influence functions
- Hampel, Ronchetti, et al.
- 1986
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Citation Context ...ting quantity depends only on the distribution F , denoted by T (F ). As a result, a statistical estimator can be viewed as a functional mapping the space of distribution functions to Euclidean space =-=[12]-=-. For example, suppose X ∈ R1 and T (x1, . . . , xn) = ∑n i=1 xi/n is the sample mean, then T (F ) = ∫ xf(x)dx = EFX, the expectation of F , given that EFX exists. Another example is the median: T (x1... |

814 | Convergence of Stochastic Processes - Pollard - 1984 |

619 | Calibrating noise to sensitivity in private data analysis
- Dwork, McSherry, et al.
- 2006
(Show Context)
Citation Context ...mposition theorems for PTR mechanisms. 1 Introduction and Background 1.1 Differential Privacy Over the last few years a new approach to privacy-preserving data analysis, based on differential privacy =-=[8, 5]-=-, has born fruit [9, 2, 8, 1, 17, 16, 3, 14]. Intuitively, this notion says that any possible outcome of an analysis should be “almost” equally likely, independent of whether any individual opts in to... |

618 | Differential privacy
- Dwork
- 2006
(Show Context)
Citation Context ...mposition theorems for PTR mechanisms. 1 Introduction and Background 1.1 Differential Privacy Over the last few years a new approach to privacy-preserving data analysis, based on differential privacy =-=[8, 5]-=-, has born fruit [9, 2, 8, 1, 17, 16, 3, 14]. Intuitively, this notion says that any possible outcome of an analysis should be “almost” equally likely, independent of whether any individual opts in to... |

406 |
On the mathematical f'oundations of theoretical statistics
- Fisher
- 1921
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Citation Context ...he most efficient estimator of the mean of a normal distribution, under these ideal conditions, signifying that this estimator converges more quickly than any other as the number of samples increases =-=[10]-=-. On the other hand, a single very wild data point can move the sample mean arbitrarily. A much more robust estimator of location is the sample median, which is a better choice when the samples may co... |

227 | Convex Analysis and Nonlinear Optimization. Theory and Examples
- Borwein, Lewis
- 2005
(Show Context)
Citation Context ... if f is convex and differentiable at β, then ∂f(β) = {df/dβ}, a set with a single element. A result in convex optimization gives the characterization of the minimum of f in terms of ∂f : Theorem 20 (=-=[4]-=-). For any convex function f and β ∈ Domain(f), β is a global minimizer of f if and only if 0 ∈ ∂f(β). The next question is how to compute ∂fD(β). For β in the interior of a region, fD(β) is linear in... |

217 | Practical privacy: the SuLQ framework
- Blum, Dwork, et al.
(Show Context)
Citation Context ...PTR mechanisms. 1 Introduction and Background 1.1 Differential Privacy Over the last few years a new approach to privacy-preserving data analysis, based on differential privacy [8, 5], has born fruit =-=[9, 2, 8, 1, 17, 16, 3, 14]-=-. Intuitively, this notion says that any possible outcome of an analysis should be “almost” equally likely, independent of whether any individual opts in to, or opts out of, the data set. Still speaki... |

217 | A learning theory approach to non-interactive database privacy
- Blum, Ligett, et al.
(Show Context)
Citation Context ...PTR mechanisms. 1 Introduction and Background 1.1 Differential Privacy Over the last few years a new approach to privacy-preserving data analysis, based on differential privacy [8, 5], has born fruit =-=[9, 2, 8, 1, 17, 16, 3, 14]-=-. Intuitively, this notion says that any possible outcome of an analysis should be “almost” equally likely, independent of whether any individual opts in to, or opts out of, the data set. Still speaki... |

203 | Mechanism design via differential privacy
- McSherry, Talwar
(Show Context)
Citation Context ...PTR mechanisms. 1 Introduction and Background 1.1 Differential Privacy Over the last few years a new approach to privacy-preserving data analysis, based on differential privacy [8, 5], has born fruit =-=[9, 2, 8, 1, 17, 16, 3, 14]-=-. Intuitively, this notion says that any possible outcome of an analysis should be “almost” equally likely, independent of whether any individual opts in to, or opts out of, the data set. Still speaki... |

164 | Smooth sensitivity and sampling in private data analysis
- Nissim, Raskhodnikova, et al.
- 2007
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144 | Our data, ourselves: Privacy via distributed noise generation
- Dwork, Kenthapadi, et al.
- 2006
(Show Context)
Citation Context ... other composition results in the literature. 1.6 Related Work The most relevant related privacy results are the definitions of differential privacy [8, 5], its relaxation (ε, δ)-differential privacy =-=[7]-=-, and the calibration of noise to sensitivity for maintaining privacy, already discussed [8]. Also mentioned above is the idea of calibrating noise to (something related to) local sensitivity, rather ... |

102 | Privacy-preserving datamining on vertically partitioned databases - Dwork, Nissim - 2004 |

97 | What can we learn privately
- Kasiviswanathan, Lee, et al.
- 2008
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96 |
consistency too: a holistic solution to contingency table release. InPODS
- Privacy
- 2007
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20 | An ad omnia approach to defining and achieving private data analysis. InPinKDD
- Dwork
- 2007
(Show Context)
Citation Context ...onal power. Differential privacy is also an ad omnia (rather than ad hoc) guarantee, and addresses any concerns that an individual might have about allowing her data to be included in a database (see =-=[6]-=- for further discussion of this point). The key result for differential privacy is due to Dwork, McSherry, Nissim, and Smith [8]. For this, we require some definitions. Definition 4. For f : D → Rd, t... |

20 | Efficient, differentially private point estimators
- Smith
- 2008
(Show Context)
Citation Context ...acy, already discussed [8]. Also mentioned above is the idea of calibrating noise to (something related to) local sensitivity, rather than global sensitivity [17]. In parallel with our efforts, Smith =-=[19]-=- investigated maximum likelihood estimators, showing that for well-behaved parametric probability models, one can construct an estimator whose distribution converges to that of the MLE. In particular,... |

14 |
WOLFOWITZ(1958) .On the deviations of the empiric distribution function of vector chance variables .Transactj
- KIEFER
(Show Context)
Citation Context ... /∈ (lj , rj)) =PF (qj(D) ≤ lj) + P (qj(D) ≥ rj) ≤2PF (sup x |F (x)− Fn(x)| ≥ n−1/3ξ) ≤2c1e−c2n1/3 , the last inequality is a well known result about the deviations of the empirical distribution (see =-=[15]-=-), where c1 and c2 are numerical constants depending only on F , and they may take different value when they appear in different places throughout this paper. Therefore we have PF (E1) ≥ 1− c1e−c2n1/3... |

4 |
On the histogram as a density estimator: L2 theory. Z. Wahrscheinlichkeitstheorie verw. Gebeite 57:453–476
- Freedman, Diaconis
- 1981
(Show Context)
Citation Context ...for any > 0, there exists M , such that P (|an| > M) < for all n. In addition, if an, bn are two random sequences we say an = OP (bn) if an/bn = OP (1). 4 The scale The interquartile range (IQR) (=-=[11]-=-) is a well-known robust estimate for the scale (dispersion) of the data, and is used in applications such as histogram construction9. We give a simple algorithm for differentially private release of ... |