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problem: Minor corrections

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Manos Katsomallos 2021-10-25 05:06:25 +02:00
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text/problem/thething/problem.tex
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@ -6,10 +6,13 @@ In this section, we introduce a new privacy definition.
\subsubsection{Setting} \subsubsection{Setting}
\label{subsec:lmdk-set} \label{subsec:lmdk-set}
Our problem setting consists of three entities: (i)~data generators (users), (ii)~data publishers (trusted non-adversarial entities), and (iii)~data consumers (possibly adversarial entities). Our problem setting consists of three entities: (i)~data generators (users), (ii)~data publishers (trusted non-adversarial entities), and (iii)~data consumers (possibly adversarial entities).
Users generate sensitive data, which are processed in a secure and private way by a trusted curator and are later published in order to be consumed by potentially adversarial data analysts. Users generate a finite series of sensitive data over time, which are processed in batch mode in a secure and private way locally (or by a trusted curator) and are later published in order to be consumed by potentially adversarial data analysts.
%The data unit produced by the users is an \emph{event}, i.e., a piece of timestamped user-related information.\kat{should we say geo-stamped?}.
Data are produced as a series of events, which we call time series. Data are produced as a series of events, which we call time series.
An \emph{event} is defined as a triple of an identifying attribute of an individual and the possibly sensitive data at a timestamp.
% Users generate sensitive data, which are processed in a secure and private way by a trusted curator and are later published in order to be consumed by potentially adversarial data analysts.
%The data unit produced by the users is an \emph{event}, i.e., a piece of timestamped user-related information.\kat{should we say geo-stamped?}.
% Data are produced as a series of events, which we call time series.
% An \emph{event} is defined as a triple of an identifying attribute of an individual and the possibly sensitive data at a timestamp.
%This workflow is repeated in a continuous manner, producing series of events, which we call time series. %This workflow is repeated in a continuous manner, producing series of events, which we call time series.
%, producing, processing, publishing, and consuming events in a private manner. %, producing, processing, publishing, and consuming events in a private manner.
\begin{enumerate}[(i)] \begin{enumerate}[(i)]
@ -82,7 +85,7 @@ Theorem~\ref{theor:thething-prv} states how to achieve the desired privacy goal
\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 $(\varepsilon, L)$-\emph{{\thething} privacy} if for any $t$ it holds that
$$ \sum_{i\in L \cup \{t\}} \varepsilon_i \leq \varepsilon$$ $$ \sum_{i\in L \cup \{t\}} \varepsilon_i \leq \varepsilon$$
\end{theorem} \end{theorem}