Privacy amplification by subsampling

\(\epsilon' = \log(1 + q(e^\epsilon - 1))\), which for small epsilon is close to \(q\epsilon\) – running a mechanism on a q-fraction of the data buys roughly a factor q of privacy.

Usage

morie_privacy_amplification(epsilon, q, delta = 0)

Arguments

epsilon

base epsilon.

q

sampling rate in (0, 1].

delta

base delta.

Value

list with epsilon_amplified, delta_amplified, ratio, linear_approx.

Details

The amplification is real only for a SECRET, freshly drawn subsample. If the sample is fixed, published, or inferable, there is no amplification at all and the claimed epsilon is simply wrong.

References

Balle, B., Barthe, G. and Gaboardi, M. (2018). Privacy amplification by subsampling. NeurIPS, 6277-6287.

Examples

round(morie_privacy_amplification(1, 0.01)$epsilon_amplified, 5)
#> [1] 0.01704