DPMechBernstein-class function

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. class

## S4 method for signature 'DPMechBernstein'
show(object)

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

## S4 method for signature '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.

Returns

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_.

Examples

## See the bernstein vignette

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.