sensitivitySampler-DPMech-function-numeric-method function

Sensitivity sampler for DPMech-class's.

Given a constructed DPMech-class, complete with target

function and sensitivityNorm, and an oracle for producing records, samples the sensitivity of the target function to set the mechanism's sensitivity. methods

## S4 method for signature 'DPMech,`function`,numeric'
sensitivitySampler(object, oracle, n,
  m = NA_integer_, gamma = NA_real_)

Arguments

• object: an object of class DPMech-class.
• oracle: a source of random databases. A function returning: list, matrix/data.frame (data in rows), numeric/character vector of records if given desired length > 1; or single record given length 1, respectively a list element, a row/named row, a single numeric/character. Whichever type is used should be expected by object@target.
• n: database size scalar positive numeric, integer-valued.
• m: sensitivity sample size scalar positive numeric, integer-valued.
• gamma: RDP privacy confidence level.

Returns

object with updated gammaSensitivity slot.

Examples

## Simple example with unbounded data hence no global sensitivity.
f <- function(xs) mean(xs)
m <- DPMechLaplace(target = f, dims = 1)
m@sensitivity ## Inf
m@gammaSensitivity ## NA as Laplace is naturally eps-DP
P <- function(n) rnorm(n)
m <- sensitivitySampler(m, oracle = P, n = 100, gamma = 0.33)
m@sensitivity ## small like 0.03...
m@gammaSensitivity ## 0.33 as directed, now m is (eps,gam)-DP.

References

Benjamin I. P. Rubinstein and Francesco Aldà. "Pain-Free Random Differential Privacy with Sensitivity Sampling", accepted into the 34th International Conference on Machine Learning (ICML'2017), May 2017.