In privacytoolsproject/PSI-Library: Differentially Private Statistical Releases for Privacy Preservation

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Differentially Private Variance with dpVariance

The dpVariance class evaluates a privacy-preserving variance of a vector of values. The class supports any vector type that can be represented numerically, meaning that it can handle the R types numeric, integer, and logical.

Syntax

# import the library
library(PSIlence)

# example data
x1 <- c(3, 12, 20, 42, 33, 65, 70, 54, 33, 45)
x2 <- c(TRUE, FALSE, FALSE, TRUE, FALSE, TRUE, TRUE, TRUE, FALSE, TRUE)
data <- data.frame(x1, x2)

# example on a numeric variable
dpVarianceExample <- dpVariance$new(mechanism='mechanismLaplace', varType='numeric',
                      variable='x1', epsilon=10, n=10, rng=c(0, 70))
dpVarianceExample$release(data)
print(dpVarianceExample$result)

# example on a logical variable
dpVarianceExample2 <- dpVariance$new(mechanism='mechanismLaplace', varType='logical',
                       variable='x2', epsilon=0.1, n=10, rng=c(0, 1))
dpVarianceExample2$release(data)
print(dpVarianceExample2$result)

Arguments

In typical usage, there are two methods to the dpVariance class: the new method and the release method. The new method does not touch any data, it just creates an object that can calculate a differentially private covariance matrix. Only the release method touches data, and applies the functionality of the previously created object to the data.

• mechanism \ Character, the class name of the mechanism used to perturb the true estimate, must be 'mechanismLaplace'.

• varType \ Character, the type of values in the data frame that will be passed to the mechanism. Should be one of 'numeric', 'integer', or 'logical'.

• variable \ character, the name of the variable in the data for which to calculate the variance.

• n \ Integer, the number of observations in the vector.

• rng \ Numeric, a 2-tuple giving an a priori estimate of the lower and upper bounds of the vector.

• epsilon \ Numeric, the differential privacy parameter $\epsilon$, typically taking values between 0 and 1 and reflecting the privacy cost of the query. Optional, default NULL. If NULL, the user must specify a value for accuracy.

• accuracy \ Numeric, the accuracy of the query. Optional, default NULL. If NULL, the user must specify a value for epsilon. If epsilon is not NULL, this value is ignored and evaluated internally.

• imputeRng \ Numeric, a 2-tuple giving a range within which missing values of the vector are imputed. Optional, default NULL. If NULL, missing values are imputed using the range provided in rng. See Notes below for more information.

• alpha \ Numeric, the statistical significance level used in evaluating accuracy and privacy parameters. If the bootstrap is employed, alpha is also used to trim the release. Default 0.05.

 

The release method accepts a single argument.

• data \ Data frame containing numeric columns corresponding the name specified in variable.

Values

The release method makes a call to the mechanism, which generates a list of statistical summaries available on the result field.

• result List, contains the accuracy guarantee, privacy cost, and private release. Other elements reflecting variable post-processing of the release are also included.

 

The list in the result attribute has the following values.

• release \ Differentially private estimate of the variance.
• variable \ The variable n the data for which the differentially private variance was calculated.
• std \ Differentially private estimate of the standard deviation of the variable (the square root of the variance estimate).
• accuracy \ The accuracy guarantee of the release, given epsilon, if epsilon was entered. Otherwise, this is the accuracy value entered by the user.
• epsilon \ The privacy cost required to guarantee accuracy, if accuracy was entered. Otherwise, this is the epsilon value entered by the user.

 

Examples

Import the PSIlence library and attach the sample dataset:

library(PSIlence)
data(PUMS5extract10000)

 

Numeric Example

To calculate a private variance of a numeric vector with dpVariance, enter the mechanism (this will be the Laplace Mechanism, or 'mechanismLaplace'), the variable type ('numeric'), the variable of interest (the column name of the variable in the dataframe), the number of observations in the dataframe, the epsilon value (generally less than 1), and the range:

numericVariance <- dpVariance$new(mechanism='mechanismLaplace', varType='numeric',
                           variable='income', n=10000, epsilon=0.1, rng=c(0, 750000))
numericVariance$release(PUMS5extract10000)
print(numericVariance$result)

 

Logical Example

To calculate the variance of a logical variable, input a the name of a logical vector into variable and update varType to 'logical'. Note: you do not need to enter a range for a logical variable (because the range is known to be c(0,1)).

logicalVariance <- dpVariance$new(mechanism='mechanismLaplace', varType='logical',
                           variable='married', n=10000, epsilon=0.1, rng=c(0, 1))
logicalVariance$release(PUMS5extract10000)
print(logicalVariance$result)

Notes

• For the imputeRng argument, the imputation strategy is to use a Uniform distribution to choose any value in the imputation range with equal probability.

privacytoolsproject/PSI-Library documentation built on Feb. 17, 2020, 2:03 p.m.