pooledCovDataAccess {DPpack}R Documentation

Differentially Private Pooled Covariance Data Access Function

Description

This function performs the data access step in the computation of a differentially private pooled covariance. The true values are computed using the theoretical formula and cov, while the sensitivities are calculated based on bounded and unbounded differential privacy (Kifer and Machanavajjhala 2011) according to the theoretical values (Liu 2019).

Usage

pooledCovDataAccess(
  samples,
  lower.bound1,
  upper.bound1,
  lower.bound2,
  upper.bound2,
  approx.n.max
)

Arguments

samples

List of two-column matrices from which to compute the pooled covariance.

lower.bound1, lower.bound2

Real numbers giving the lower bounds of the first and second columns of samples, respectively.

upper.bound1, upper.bound2

Real numbers giving the upper bounds of the first and second columns of samples, respectively.

approx.n.max

Logical indicating whether to approximate n.max, which is defined to be the length of the largest input vector. Approximation is best if n.max is very large.

Value

List of the true pooled covariance and the sensitivities calculated based on bounded and unbounded differential privacy.

References

Liu F (2019). “Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints.” Transactions on Data Privacy, 12(3), 169-195. http://www.tdp.cat/issues16/tdp.a316a18.pdf.

Kifer D, Machanavajjhala A (2011). “No Free Lunch in Data Privacy.” In Proceedings of the 2011 ACM SIGMOD International Conference on Management of Data, SIGMOD '11, 193–204. ISBN 9781450306614, doi:10.1145/1989323.1989345.

Examples

x1 <- matrix(c(1,4,-2,8,-6,-3),ncol=2)
x2 <- matrix(c(1,2,-5,7),ncol=2)
pooledCovDataAccess(list(x1,x2),-10,10,-10,10,FALSE)


[Package DPpack version 0.2.0 Index]