An S4 class for the Bernstein mechanism of differential privacy.

A class that implements the Bernstein mechanism (not iterated version) of differential privacy, for privatizing release of real-valued functions on \([0,1]^l\) based on arbitrary datasets. Approximates the target on a lattice.

# S4 method for DPMechBernstein
show(object)

# S4 method for DPMechBernstein,DPParamsEps
releaseResponse(mechanism,
  privacyParams, X)

# S4 method for DPMechBernstein
sensitivityNorm(mechanism, X1, X2)

Arguments

object

an instance of class DPMech.
mechanism

an object of class DPMechBernstein.
privacyParams

an object of class DPParamsEps.
X

a privacy-sensitive dataset, if using sensitivity sampler a: list, matrix, data frame, numeric/character vector.
X1

a privacy-sensitive dataset.
X2

a privacy-sensitive dataset.

Value

list with slots per argument, actual privacy parameter and response: mechanism response with length of target release: privacyParams, sensitivity, latticeK, dims, target, response.

scalar numeric norm of non-private target on datasets. The \(L_\infty\) of the functions on a lattice.

Methods (by generic)

  • show: automatically prints the object.

  • releaseResponse: releases Bernstein mechanism responses.

  • sensitivityNorm: measures target sensitivity.

Slots

sensitivity

non-negative scalar numeric maximum absolute target sensitivity maximized over the lattice. Defaults to Inf for use with sensitivitySampler().

target

might be a closure that takes arbitrary dataset and returns a real-valued function on \([0,1]^l\).

gammaSensitivity

NA_real_ if inactive, or scalar in [0,1) indicating that responses must be RDP with specific confidence.

latticeK

positive scalar integer-valued numeric specifying the lattice resolution. Defaults to (invalid) NA_integer_.

dims

positive scalar integer-valued numeric specifying the dimension of released function domain. Defaults to (invalid) NA_integer_.

References

Francesco Aldà and Benjamin I. P. Rubinstein. "The Bernstein Mechanism: Function Release under Differential Privacy", in Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI'2017), pp. 1705-1711, Feb 2017.

Examples

## See the bernstein vignette