Gaussian mechanism for differential privacy

The bound is only valid for epsilon below one, which is checked rather than assumed; the noise is drawn from the deterministic inverse-normal stream so the released value is reproducible across language arms.

Usage

Gaussm(f_value, l2_sens, epsilon, delta, draw = 1)

Arguments

f_value: Query value(s) to release.
l2_sens: L2 sensitivity of the query, positive.
epsilon: Privacy parameter in (0, 1).
delta: Failure probability in (0, 1).
draw: Index into the deterministic noise stream.

Value

List with estimate, released, noise, sigma, c, epsilon, delta, n, method.

Details

Formula: M(D) = f(D) + N(0, sigma^2) with sigma = sqrt(2 log(1.25/delta)) Delta_2 f / epsilon.

References

Dwork and Roth (2014), The Algorithmic Foundations of Differential Privacy, Foundations and Trends in Theoretical Computer Science 9(3-4):211-407, Theorem A.1. doi:10.1561/0400000042

Examples

Gaussm(c(1, 2, 3), l2_sens = 1, epsilon = 0.5, delta = 1e-5)
#> $estimate
#> [1] -5.535543
#> 
#> $released
#> [1] -5.535543  8.535543 -8.146437
#> 
#> $noise
#> [1]  -6.535543   6.535543 -11.146437
#> 
#> $sigma
#> [1] 9.689611
#> 
#> $c
#> [1] 4.844805
#> 
#> $epsilon
#> [1] 0.5
#> 
#> $delta
#> [1] 1e-05
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "f(D) + N(0, sigma^2) with sigma = sqrt(2 ln(1.25/delta)) Delta_2 f / eps, Dwork & Roth (2014) Thm A.1"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"