sdDP: Differentially Private Standard Deviation

In DPpack: Differentially Private Statistical Analysis and Machine Learning

Differentially Private Standard Deviation

Description

This function computes the differentially private standard deviation of a given dataset at user-specified privacy levels of epsilon and delta.

Usage

sdDP(
  x,
  eps,
  lower.bound,
  upper.bound,
  which.sensitivity = "bounded",
  mechanism = "Laplace",
  delta = 0,
  type.DP = "aDP"
)

Arguments

x	Numeric vector whose variance is desired.
eps	Positive real number defining the epsilon privacy budget.
lower.bound	Scalar representing the global or public lower bound on values of x.
upper.bound	Scalar representing the global or public upper bound on values 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, delta)-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: 'Laplace', 'Gaussian'. Default is Laplace. See LaplaceMechanism and GaussianMechanism for a description of the supported mechanisms.
delta	Nonnegative real number defining the delta privacy parameter. If 0 (default), reduces to eps-DP and the Laplace mechanism is used.
type.DP	String indicating the type of differential privacy desired for the Gaussian mechanism (if selected). Can be either 'pDP' for probabilistic DP \insertCiteMachanavajjhala2008DPpack or 'aDP' for approximate DP \insertCiteDwork2006bDPpack. Note that if 'aDP' is chosen, epsilon must be strictly less than 1.

Value

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

References

\insertRef

Dwork2006aDPpack

\insertRef

Kifer2011DPpack

\insertRef

Machanavajjhala2008DPpack

\insertRef

Dwork2006bDPpack

\insertRef

Liu2019bDPpack

Examples

D <- stats::rnorm(500, mean=3, sd=2)
lb <- -3 # 3 std devs below mean
ub <- 9 # 3 std devs above mean
sdDP(D, 1, lb, ub)
sdDP(D,.5, lb, ub, which.sensitivity='unbounded', mechanism='Gaussian',
  delta=0.01)

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