Samples a candidate with probability proportional to
\(\exp(\epsilon u / 2\Delta u)\).
Usage
morie_dp_exponential_mechanism(
candidates,
utility,
epsilon = 1,
sensitivity = 1,
seed = NULL
)
Arguments
- candidates
vector or list of candidates.
- utility
utility of each candidate, finite.
- epsilon
privacy budget.
- sensitivity
sensitivity of the utility function.
- seed
optional integer seed.
Value
list with selected, index (0-based, matching the
Python module), probabilities.
Details
This is the mechanism for choices rather than numbers – where adding
noise to the answer makes no sense because the answer is not a number.
The 2 in the denominator is load-bearing: it is what covers the change
in the normalising constant as well as in the utility, and dropping it
halves the claimed epsilon.
References
McSherry, F. and Talwar, K. (2007). Mechanism design via
differential privacy. FOCS, 94-103.
Examples
r <- morie_dp_exponential_mechanism(c("a", "b", "c"), c(0, 5, 1),
epsilon = 2, seed = 1
)
round(r$probabilities, 3)
#> [1] 0.007 0.976 0.018
