DPMechExponential-class function

An S4 class for the exponential mechanism of differential privacy.

A class that implements the exponential mechanism of differential privacy, for privatizing releases from sets (not necessarily numeric as required by DPMechLaplace). Currently limited to responses from a finite sets - the most widely used case - as these induce easily computed sampling distributions from a uniform base measure. class

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

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

## S4 method for signature 'DPMechExponential'
sensitivityNorm(mechanism, X1, X2)

Arguments

• object: an instance of class DPMech.
• mechanism: an object of class DPMechExponential.
• 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, responseSet, target, response.

scalar numeric norm of non-private target on datasets.

Methods (by generic)

• show: automatically prints the object.
• releaseResponse: releases exponential mechanism responses.
• sensitivityNorm: measures target quality score sensitivity.

Slots

• sensitivity: non-negative scalar numeric quality function sensitivity. Defaults to Inf for use with sensitivitySampler().
• target: the quality score function mapping dataset to a function on responses (elements of responseSet).
• gammaSensitivity: NA_real_ if inactive, or scalar in [0,1) indicating that responses must be RDP with specific confidence.
• responseSet: a list of possible responses of the mechanism.

Examples

## Sensitive data are strings of length at most 5.
## Task is to release most frequent character present, hence quality function
## is a closure that counts character frequencies for given candidate char.
## Global sensitivity is max string length.
qualF <- function(X) { function(r) sum(r == unlist(strsplit(X, ""))) }
rs <- as.list(letters)
m <- DPMechExponential(sensitivity = 5, target = qualF, responseSet = rs)
X <- strsplit("the quick brown fox jumps over the lazy dog"," ")[[1]]
p <- DPParamsEps(epsilon = 1)
releaseResponse(m, p, X)

References

Frank McSherry and Kunal Talwar. "Mechanism design via differential privacy." In the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07), pp. 94-103. IEEE, 2007.