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thething: Reviwed def:thething-prv

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Manos Katsomallos 2021-09-19 23:36:18 +02:00
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text/problem/thething/problem.tex
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@ -139,8 +139,8 @@ We proceed to propose \emph{{\thething} privacy}, a configurable variation of di
\begin{definition} \begin{definition}
% [{\Thething} privacy] % [{\Thething} privacy]
\label{def:thething-prv} \label{def:thething-prv}
Let $\mathcal{M}$ be a privacy mechanism with range $\mathcal{O}$ and domain $\mathcal{S}_T$ being the set of all time series with length $|T|$, where $T$ is a sequence of timestamps. Let $\mathcal{M}$ be a privacy mechanism with range $\mathcal{O}$ that takes as input a time series.
$\mathcal{M}$ satisfies {\thething} $\varepsilon$-differential privacy (or, simply, {\thething} privacy) if for all sets $O \subseteq \mathcal{O}$, and for every pair of {\thething}-neighboring time series $S_T$, $S_T'$, We say that $\mathcal{M}$ satisfies {\thething} $\varepsilon$-differential privacy (or, simply, {\thething} privacy) if for all sets of possible outputs $O \subseteq \mathcal{O}$, and for every pair of {\thething}-neighboring time series $S_T$, $S_T'$,
% and all $T = (t)_{t \in \mathbb{N}}$, % and all $T = (t)_{t \in \mathbb{N}}$,
it holds that it holds that
$$Pr[\mathcal{M}(S_T) \in O] \leq e^\varepsilon Pr[\mathcal{M}(S_T') \in O]$$ $$Pr[\mathcal{M}(S_T) \in O] \leq e^\varepsilon Pr[\mathcal{M}(S_T') \in O]$$