medianDP: Differentially Private Median

In DPpack: Differentially Private Statistical Analysis and Machine Learning

Differentially Private Median

Description

This function computes the differentially private median of an input vector at a user-specified privacy level of epsilon.

Usage

medianDP(
  x,
  eps,
  lower.bound,
  upper.bound,
  which.sensitivity = "bounded",
  mechanism = "exponential",
  uniform.sampling = TRUE
)

Arguments

x	Numeric vector of which the median will be taken.
eps	Positive real number defining the epsilon privacy budget.
lower.bound	Real number giving the global or public lower bound of x.
upper.bound	Real number giving the global or public upper bound of x.
which.sensitivity	String indicating which type of sensitivity to use. Can be one of 'bounded', 'unbounded', 'both'. If 'bounded' (default), returns result based on bounded definition for differential privacy. If 'unbounded', returns result based on unbounded definition. If 'both', returns result based on both methods \insertCiteKifer2011DPpack. Note that if 'both' is chosen, each result individually satisfies (eps, 0)-differential privacy, but may not do so collectively and in composition. Care must be taken not to violate differential privacy in this case.
mechanism	String indicating which mechanism to use for differential privacy. Currently the following mechanisms are supported: 'exponential'. See ExponentialMechanism for a description of the supported mechanisms.
uniform.sampling	Boolean indicating whether to sample uniformly between sorted dataset values when returning the private quantile. If TRUE, it is possible for this function to return any number between lower.bound and upper.bound. If FALSE, only a value present in the dataset or the lower bound can be returned.

Value

Sanitized median based on the bounded and/or unbounded definitions of differential privacy.

References

\insertRef

Dwork2006aDPpack

\insertRef

Kifer2011DPpack

\insertRef

Smith2011aDPpack

Examples

D <- stats::rnorm(500)
lower.bound <- -3 # 3 standard deviations below mean
upper.bound <- 3 # 3 standard deviations above mean

eps <- 1
# Get median satisfying pure 1-differential privacy
private.median <- medianDP(D, eps, lower.bound, upper.bound)
private.median

# Require released value to be in dataset
private.median <- medianDP(c(1,0,3,3,2), eps, 0, 4, uniform.sampling = FALSE)
private.median

DPpack documentation built on April 8, 2023, 9:09 a.m.