pooledCovDP: Differentially Private Pooled Covariance

In DPpack: Differentially Private Statistical Analysis and Machine Learning

Differentially Private Pooled Covariance

Description

This function computes the differentially private pooled covariance from two or more two-column matrices of data at user-specified privacy levels of epsilon and delta.

Usage

pooledCovDP(
  ...,
  eps = 1,
  lower.bound1,
  upper.bound1,
  lower.bound2,
  upper.bound2,
  which.sensitivity = "bounded",
  mechanism = "Laplace",
  delta = 0,
  type.DP = "aDP",
  approx.n.max = FALSE
)

Arguments

...	Two or more matrices, each with two columns from which to compute the pooled covariance.
eps	Positive real number defining the epsilon privacy budget.
lower.bound1, lower.bound2	Real numbers giving the global or public lower bounds over the first and second columns of all input data, respectively.
upper.bound1, upper.bound2	Real numbers giving the global or public upper bounds over the first and second columns of all input data, respectively.
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.
approx.n.max	Logical indicating whether to approximate n.max (defined to be the length of the largest input vector) in the computation of the global sensitivity based on the upper and lower bounds of the data \insertCiteLiu2019bDPpack. Approximation is best if n.max is very large.

Value

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

References

\insertRef

Dwork2006aDPpack

\insertRef

Kifer2011DPpack

\insertRef

Machanavajjhala2008DPpack

\insertRef

Dwork2006bDPpack

\insertRef

Liu2019bDPpack

Examples

# Build datasets
D1 <- sort(stats::rnorm(500, mean=3, sd=2))
D2 <- sort(stats::rnorm(500, mean=-1, sd=0.5))
D3 <- sort(stats::rnorm(200, mean=3, sd=2))
D4 <- sort(stats::rnorm(200, mean=-1, sd=0.5))
M1 <- matrix(c(D1, D2), ncol=2)
M2 <- matrix(c(D3, D4), ncol=2)

lb1 <- -3 # 3 std devs below mean
lb2 <- -2.5 # 3 std devs below mean
ub1 <- 9 # 3 std devs above mean
ub2 <- .5 # 3 std devs above mean
# Pooled covariance satisfying (1,0)-differential privacy
private.pooled.cov <- pooledCovDP(M1, M2, eps = 1, lower.bound1 = lb1,
                                  lower.bound2 = lb2, upper.bound1 = ub1,
                                  upper.bound2 = ub2)
private.pooled.cov

# Pooled covariance satisfying approximate (0.9, 0.01)-differential privacy
# and approximating n.max in the sensitivity calculation
private.pooled.cov <- pooledCovDP(M1, M2, eps = 0.9, lower.bound1 = lb1,
                                  lower.bound2 = lb2, upper.bound1 = ub1,
                                  upper.bound2 = ub2, mechanism = 'Gaussian',
                                  delta = 0.01, approx.n.max = TRUE)
private.pooled.cov

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