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

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Differentially Private Mean with dpMean

The dpMean class evaluates a privacy-preserving mean 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

library(PSIlence)
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)

dpMeanExample <- dpMean$new(mechanism='mechanismLaplace', varType='numeric', 
                      variable='x1', epsilon=0.1, n=10, rng=c(0, 70))
out <- dpMeanExample$release(data)
dpMeanExample2 <- dpMean$new(mechanism='mechanismLaplace', varType='logical', variable='x2', epsilon=0.1, n=10)
out2 <- dpMeanExample2$release(data)

Arguments

In typical usage, there are two methods to the dpGLM class. The new method, which creates an object of the class, accepts the following arguments.

• mechanism \ Character, the class name of the mechanism used to perturb the true estimate, one of 'mechanismLaplace' or 'mechanismBootstrap'.

• 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'.

• 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.

• nBoot \ Integer, the number of bootstrap replications to perform. Optional, default NULL. If not NULL, the privacy cost epsilon is partitioned across nBoot replications and the estimates for each are returned.

• 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.

• x \ Data frame containing numeric columns corresponding the names specified in formula.

Examples

Attach the sample dataset.

library(PSIlence)
data(PUMS5extract10000)

 

Calculate a private mean of a numeric vector with dpMean using the Laplace mechanism:

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

 

To calculate the mean of a logical vector instead, input a logical vector into x and update varType and rng appropriately:

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

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.

 

The list in the result attribute has the following values.

• release \ Differentially private estimate of the mean. If the bootstrap mechanism is used, one estimate for each bootstrap replication is provided (i.e., vector of length nBoot).
• accuracy \ The accuracy guarantee of the release given epsilon.
• epsilon \ The privacy cost required to guarantee accuracy.
• interval \ Confidence interval of the private estimate given accuracy.
• std.dev \ The standard deviation of the vector. Only available for logical vectors.
• median \ The median of the vector. Only available for logical vectors.
• histogram \ The histogram of the vector. Only available for logical vectors.
• std.error \ Estimates of the standard error of the mean. Only available when the bootstrap mechanism is used.

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