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privacy: Minor corrections

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Manos Katsomallos 2022-01-15 03:36:45 +01:00
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text/preliminaries/privacy.tex
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@ -340,9 +340,9 @@ The technique adds random noise drawn from a multivariate Laplace distribution t
\label{fig:mech-planar-lap} \label{fig:mech-planar-lap}
\end{figure} \end{figure}
For query functions that do not return a real number, e.g.,~`What is the most visited country this year?' or in cases where perturbing the value of the output will completely destroy its utility, e.g.,~`How many patients in the ICU?' most works in the literature use the \emph{Exponential mechanism}~\cite{mcsherry2007mechanism}. For query functions that do not return a real number, e.g.,~`What is the most visited country this year?', or in cases where perturbing the value of the output will completely destroy its utility, e.g.,~`How many patients in the ICU?', most works in the literature use the \emph{Exponential mechanism}~\cite{mcsherry2007mechanism}.
Initially, a utility function $u$, with sensitivity $\Delta u$, maps pairs of the input value $x$ and output value $r$ to utility scores. Initially, a utility function $u$, with sensitivity $\Delta u$, maps pairs of the input value $x$ and output value $r$ to utility scores.
Thereafter, the mechanism $M$ selects an output value $r$ from a set of possible outputs $R$ with probability proportional to $\exp(\frac{\varepsilon u(x, r)}{2\Delta u})$ (Figure~\ref{fig:mech-exp}). Thereafter, the mechanism $M$ selects an output value $r$ from a set of possible outputs $R$ with probability proportional to $\exp(\frac{\varepsilon u(x, r)}{2\Delta u})$.
% $\Delta u$is the sensitivity of the utility % $\Delta u$is the sensitivity of the utility
% \kat{what is the utility function?} % \kat{what is the utility function?}
% \mk{Already explained} % \mk{Already explained}