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2.2.3. comments katerina

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text/preliminaries/privacy.tex
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@ -61,15 +61,16 @@ Users are subject to privacy attacks, and thus are the main point of interest of
In more detail, the privacy protection levels are: In more detail, the privacy protection levels are:
\begin{enumerate}[(a)] \begin{enumerate}[(a)]
\item \emph{Event}~\cite{dwork2010differential, dwork2010pan}---limits the privacy protection to \emph{any single event} in a time series, providing maximum data utility. \item \emph{Event}~\cite{dwork2010differential, dwork2010pan}---limits the privacy protection to \emph{any single event} in a time series, providing maximum \kat{maximum? better say high} data utility.
\item \emph{$w$-event}~\cite{kellaris2014differentially}---provides privacy protection to \emph{any sequence of $w$ events} in a time series. \item \emph{$w$-event}~\cite{kellaris2014differentially}---provides privacy protection to \emph{any sequence of $w$ events} in a time series.
\item \emph{User}~\cite{dwork2010differential, dwork2010pan}---protects \emph{all the events} in a time series, providing maximum privacy protection. \item \emph{User}~\cite{dwork2010differential, dwork2010pan}---protects \emph{all the events} in a time series, providing maximum\kat{maximum? better say high} privacy protection.
\end{enumerate} \end{enumerate}
Figure~\ref{fig:prv-levels} demonstrates the application of the possible protection levels on the statistical data of Example~\ref{ex:continuous}. Figure~\ref{fig:prv-levels} demonstrates the application of the possible protection levels on the statistical data of Example~\ref{ex:continuous}.
For instance, in event-level (Figure~\ref{fig:level-event}) it is hard to determine whether Quackmore was dining at Opera at $t_1$. For instance, in event-level (Figure~\ref{fig:level-event}) it is hard to determine whether Quackmore was dining at Opera at $t_1$.
Moreover, in user-level (Figure~\ref{fig:level-user}) it is hard to determine whether Quackmore was ever included in the released series of events at all. Moreover, in user-level (Figure~\ref{fig:level-user}) it is hard to determine whether Quackmore was ever included in the released series of events at all.
Finally, in $2$-event-level (Figure~\ref{fig:level-w-event}) it is hard to determine whether Quackmore was ever included in the released series of events between the timestamps $t_1$ and $t_2$, $t_2$ and $t_3$, etc. (i.e.,~for a window $w = 2$). Finally, in $2$-event-level (Figure~\ref{fig:level-w-event}) it is hard to determine whether Quackmore was ever included in the released series of events between the timestamps $t_1$ and $t_2$, $t_2$ and $t_3$, etc. (i.e.,~for a window $w = 2$).
\kat{Already, by looking at the original counts, for the reader it is hard to see if Quackmore was in the event/database. So, we don't really get the difference among the different levels here.}
\begin{figure}[htp] \begin{figure}[htp]
\centering \centering
@ -82,15 +83,15 @@ Finally, in $2$-event-level (Figure~\ref{fig:level-w-event}) it is hard to deter
\subcaptionbox{$2$-event-level\label{fig:level-w-event}}{% \subcaptionbox{$2$-event-level\label{fig:level-w-event}}{%
\includegraphics[width=.32\linewidth]{level-w-event}% \includegraphics[width=.32\linewidth]{level-w-event}%
}\hspace{\fill} }\hspace{\fill}
\caption{Protecting the data of Table~\ref{tab:continuous-statistical} on (a)~event-, (b)~user-, and (c)~$2$-event-level. A suitable distortion method can be applied accordingly.} \caption{Protecting the data of Table~\ref{tab:continuous-statistical} on (a)~event-, (b)~user-, and (c)~$2$-event-level. A suitable distortion method can be applied accordingly. \kat{Why don't you distort the results already in this table?}}
\label{fig:prv-levels} \label{fig:prv-levels}
\end{figure} \end{figure}
Contrary to event-level, that provides privacy guarantees for a single event, user- and $w$-event-level offer stronger privacy protection by protecting a series of events. Contrary to event-level, which provides privacy guarantees for a single event, user- and $w$-event-level offer stronger privacy protection by protecting a series of events.
Event- and $w$-event-level handle better scenarios of infinite data observation, whereas user-level is more appropriate when the span of data observation is finite. Event- and $w$-event-level handle better scenarios of infinite data observation, whereas user-level is more appropriate when the span of data observation is finite.
$w$-event- is narrower than user-level protection due to its sliding window processing methodology. $w$-event- is narrower than user-level protection due to its sliding window processing methodology.
In the extreme cases where $w$ is equal to either $1$ or to the size of the entire length of the time series, $w$-event- matches event- or user-level protection, respectively. In the extreme cases where $w$ is equal either to $1$ or to the length of the time series, $w$-event- matches event- or user-level protection, respectively.
Although the described levels have been coined in the context of \emph{differential privacy}~\cite{dwork2006calibrating}, a seminal privacy method that we will discuss in more detail in Section~\ref{subsec:prv-statistical}, it is possible to apply their definitions to other privacy protection techniques as well. Although the described levels have been coined in the context of \emph{differential privacy}~\cite{dwork2006calibrating}, a seminal privacy method that we will discuss in more detail in Section~\ref{subsec:prv-statistical}, they are also used for other privacy protection techniques as well.
\subsection{Privacy-preserving operations} \subsection{Privacy-preserving operations}