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problem: OCD

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Manos Katsomallos 2021-10-25 01:47:21 +02:00
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text/problem/thething/problem.tex
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@ -80,7 +80,7 @@ Theorem~\ref{theor:thething-prv} states how to achieve the desired privacy goal
\begin{theorem} \begin{theorem}
[{\Thething} privacy] [{\Thething} privacy]
\label{theor:thething-prv} \label{theor:thething-prv}
Let $\mathcal{M}$ be a mechanism with input a time series $S_T$, where $T$ is the set of the involved timestamps, and $L \subseteq T$ be the set of {\thething} timestamps. Let $\mathcal{M}$ be a mechanism with input a time series $S_T$, where $T$ is the set of the involved timestamps, and $L \subseteq T$ be the set of {\thething} timestamps.
$\mathcal{M}$ is decomposed to $\varepsilon$-differential private sub-mechanisms $\mathcal{M}_t$, for every $t \in T$, which apply independent randomness to the event at $t$. $\mathcal{M}$ is decomposed to $\varepsilon$-differential private sub-mechanisms $\mathcal{M}_t$, for every $t \in T$, which apply independent randomness to the event at $t$.
Then, given a privacy budget $\varepsilon$, $\mathcal{M}$ satisfies {\thething} privacy if for any $t$ it holds that Then, given a privacy budget $\varepsilon$, $\mathcal{M}$ satisfies {\thething} privacy if for any $t$ it holds that
$$ \sum_{i\in L \cup \{t\}} \varepsilon_i \leq \varepsilon$$ $$ \sum_{i\in L \cup \{t\}} \varepsilon_i \leq \varepsilon$$