## Privacy preserving regression modelling via distributed computation (2004)

Venue: | In Proc. Tenth ACM SIGKDD Internat. Conf. on Knowledge Discovery and Data Mining |

Citations: | 22 - 9 self |

### BibTeX

@INPROCEEDINGS{Sanil04privacypreserving,

author = {Ashish P. Sanil and Alan F. Karr and Jerome P. Reiter and Xiaodong Lin and Ashish P. Sanil and Alan F. Karr and Xiaodong Lin},

title = {Privacy preserving regression modelling via distributed computation},

booktitle = {In Proc. Tenth ACM SIGKDD Internat. Conf. on Knowledge Discovery and Data Mining},

year = {2004},

pages = {677--682}

}

### Years of Citing Articles

### OpenURL

### Abstract

www.niss.org

### Citations

1870 |
Numerical recipes in C. The art of scientific computing
- Press, Teukolsky, et al.
- 1992
(Show Context)
Citation Context ...ons of the iteration block would yield the exact minimizer of f(β)! (This involves solving p(p + 1) line minimization problems to obtain the minimizer of a quadratic function.) We refer the reader to =-=[6, 5, 2]-=- for proofs and elaborations. Note In our regession case (equation (6)), the δ that minimizes E(β + δs (i) )=(y− X(β + δs (i) )) T (y − X(β + δs (i) )), is readily obtained as δ = (y − Xβ)T Xs (i) (Xs... |

323 | Algorithms for Minimization without Derivatives
- Brent
- 1973
(Show Context)
Citation Context ...ons of the iteration block would yield the exact minimizer of f(β)! (This involves solving p(p + 1) line minimization problems to obtain the minimizer of a quadratic function.) We refer the reader to =-=[3, 10, 11]-=- for proofs and elaborations. 1 Powell’s original algorithm used the coordinate axis vectors {e1, e2,...,ep} as the basis. Brent [3] shows that an arbitrary orthogonal basis also suffices. 679 Note In... |

221 |
An efficient method for finding the minimum of a function of several variables without calculating derivatives
- Powell
- 1964
(Show Context)
Citation Context ...rms the crux of our proposed method, and a protocol to compute secure sums that is an essential component of our method. 3.1 Powell’s Method for a Quadratic function of p variables Powell’s algorithm =-=[10]-=- for finding the minimizer of a function of many variables forms the basis of our proposed procedure. We will use it to directly find ˆ β as a numerical solution to the problem arg minβ∈ℜp E(β) (from ... |

211 | C.Clifton, “Privacy preserving association rule mining in vertically partitioned data
- Vaidya
(Show Context)
Citation Context ... show how to perform secure linear regression for “vertically partitioned data”. (The problem of horizontally partitioned data is addressed in a companion paper [9]). Our work is similar in spirit to =-=[12, 13]-=- who describe methods for doing cluster analysis and association rule discovery in vertically partitioned data. The recent work by Du, et al [6] for the 2-agency setting also presents a complementary ... |

198 |
Applied Linear Regression
- Weisberg
- 2005
(Show Context)
Citation Context ...g possible paths for conducting regression analyses). We end with concluding remarks in Section 6. 2. THE REGRESSION PROBLEM Consider the case when we need to fit the standard linear regression model =-=[14]-=- y = Xβ + ɛ, (1) where ⎡ ⎤ with and X =[x1 ...xp] , y = ⎡ ⎢ β = ⎣ ⎡ ⎢ xi = ⎣ β1 . βp xi1 . xin ⎢ ⎣ ⎤ ⎡ ⎥ ⎢ ⎦ , ε = ⎣ y1 . yn ⎥ ⎦ , (2) ⎤ ⎥ ⎦ , (3) ε1 . εn ⎤ ⎥ ⎦ . (4) Under the condition that ε ∼N(0,σ... |

105 |
Secret sharing homomorphisms: keeping shares of a secret secret
- Benaloh
- 1986
(Show Context)
Citation Context ...calculate v = �K j=1 vj in such a manner that each Agency j can learn only the minimum possible about the other agencies’ values, namely, the value of v(−j) = � ℓ�=j vℓ. The secure summation protocol =-=[2, 4]-=- can be used to effect this computation. Choose m to be a very large number which is known to all the agencies such that v is known to lie in the range [0,m). Agency 1 is assumed to be the leader. The... |

68 | Secure multi-party computation problems and their applications: A review and open problems
- Du, Atallah
- 2001
(Show Context)
Citation Context ...d in breaking the confidentiality of any of the others’ data. This need to balance the utility of better combined analyses with the risk of privacy violation has received considerable interest lately =-=[1, 5]-=-. Specifically, consider two cases • Vertically partioned data When multiple parties have data on certain data subjects but each party only posseses data on different sets of attributes of those entit... |

61 | Privacy-preserving multivariate statistical analysis: Linear regression and classification
- Du, Han, et al.
(Show Context)
Citation Context ...anion paper [9]). Our work is similar in spirit to [12, 13] who describe methods for doing cluster analysis and association rule discovery in vertically partitioned data. The recent work by Du, et al =-=[6]-=- for the 2-agency setting also presents a complementary approach for conducting secure linear regressions. The practical implentation of the algorithm we present is simpler since it can be implemented... |

40 |
Privacy Preserving Data Mining
- Vaidya, Clifton, et al.
- 2005
(Show Context)
Citation Context ...calculate v = �K j=1 vj in such a manner that each Agency j can learn only the minimum possible about the other agencies’ values, namely, the value of v(−j) = � ℓ�=j vℓ. The secure summation protocol =-=[2, 4]-=- can be used to effect this computation. Choose m to be a very large number which is known to all the agencies such that v is known to lie in the range [0,m). Agency 1 is assumed to be the leader. The... |

28 |
Privacy preserving kmeans clustering over vertically partitioned data
- Vidya, Clifton
(Show Context)
Citation Context ... show how to perform secure linear regression for “vertically partitioned data”. (The problem of horizontally partitioned data is addressed in a companion paper [9]). Our work is similar in spirit to =-=[12, 13]-=- who describe methods for doing cluster analysis and association rule discovery in vertically partitioned data. The recent work by Du, et al [6] for the 2-agency setting also presents a complementary ... |

27 | Secure regression on distributed databases
- Karr, Lin, et al.
(Show Context)
Citation Context ...eminated more widely. In this paper, we show how to perform secure linear regression for “vertically partitioned data”. (The problem of horizontally partitioned data is addressed in a companion paper =-=[9]-=-). Our work is similar in spirit to [12, 13] who describe methods for doing cluster analysis and association rule discovery in vertically partitioned data. The recent work by Du, et al [6] for the 2-a... |

25 | Distributed Multivariate Regression Using Wavelet-based Collective Data Mining
- Hershberger, Kargupta
- 1999
(Show Context)
Citation Context ...a in distributed databases (unencumbered by privacy concerns). There is a fairly extensive literature on this topic [8]. Some work has also been done on linear regression in distributed data settings =-=[7, 15]-=-, and it might be possible to extend some of these methods so that privacy is preserved. We view a group of government agencies seeking to perform a combined analysis on their data as a setting that r... |

5 | Distributed Regression for Heterogeneous Data Sets
- Xing, Madden, et al.
- 2003
(Show Context)
Citation Context ...a in distributed databases (unencumbered by privacy concerns). There is a fairly extensive literature on this topic [8]. Some work has also been done on linear regression in distributed data settings =-=[7, 15]-=-, and it might be possible to extend some of these methods so that privacy is preserved. We view a group of government agencies seeking to perform a combined analysis on their data as a setting that r... |

4 | Distributed data mining bibliography
- Kargupta, Liu
(Show Context)
Citation Context ...ee participating agencies. A related stream of research concerns the analysis of data in distributed databases (unencumbered by privacy concerns). There is a fairly extensive literature on this topic =-=[8]-=-. Some work has also been done on linear regression in distributed data settings [7, 15], and it might be possible to extend some of these methods so that privacy is preserved. We view a group of gove... |