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Manos Katsomallos
2021-07-18 23:07:46 +02:00
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text/related/statistical.tex
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@ -117,7 +117,7 @@ Nonetheless, as with all other similar techniques, the usage of prefix trees lim
% - \emph{Pufferfish}
% - perturbation (Laplace)
% - general (Bayesian networks/Markov chains)
\hypertarget{song2017pufferfish}{Song et al.}~\cite{song2017pufferfish} propose the \emph{Wasserstein mechanism}, a technique that applies to any general instantiation of Pufferfish (see Section~\ref{subsec:privacy-statistical}).
\hypertarget{song2017pufferfish}{Song et al.}~\cite{song2017pufferfish} propose the \emph{Wasserstein mechanism}, a technique that applies to any general instantiation of Pufferfish (see Section~\ref{subsec:prv-statistical}).
It adds noise proportional to the sensitivity of a query $F$, which depends on the worst case distance between the distributions $P(F(X)|s_i,d)$ and $P(F(X)|s_j,d)$ for a variable $X$, a pair of secrets $(s_i,s_j)$, and an evolution scenario $d$.
The Wasserstein metric function calculates the worst case distance between those two distributions.
The noise is drawn from a Laplace distribution with parameter equal to the quotient resulting from the division of the maximum Wasserstein distance of the distributions of all the pairs of secrets by the available privacy budget $\varepsilon$.