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problem: Reviewed lmdk-sel-prob

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Manos Katsomallos
2021-10-12 00:26:35 +02:00
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text/problem/theotherthing/problem.tex
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\label{subsec:lmdk-sel-prob}
The problem setting is similar to the one that we described in detail in Section~\ref{subsec:lmdk-set}.
The main difference in this case lies in our threat model where we consider, in addition to the values of the regular and {\thething} events, the {\thething} timestamps $L$ privacy-sensitive as well.
The main difference in this case lies in our threat model where we consider, in addition to the values of the regular and {\thething} events, the {\thething} timestamps $L$ as privacy-sensitive as well.
Given a set of {\thethings} at respective timestamps $\{l_k\}$ in a series of events at $\{t_n\}$, such that $\{l_k\} \subseteq \{t_n\}$, a data publisher might release this information by:
\begin{enumerate}
\item Selecting a set of options (Section~\ref{subsec:lmdk-set-opts}) consisting of different possible versions of $\{l_k\}$.
\mk{`option' or `candidate'?}
This could be:
\begin{itemize}
\item either a random set of $k$ other timestamps similar to the actual {\thething} timestamps (Section~\ref{subsec:lmdk-rnd}),
\item or a set including $\{l_k\}$ and $x \in [1, n - k]$ additional dummy timestamps (Section~\ref{subsec:lmdk-dum-gen}).
\end{itemize}
\item Releasing a privacy-preserving version of the {\thething} timestamps (Section~\ref{subsec:priv-opt-sel}).
We utilize the exponential mechanism with a utility function that calculates an indicator for each of the options in the set that we selected in the previous step.
The utility depends on the positioning of the {\thething} timestamps of an option in the series, e.g.,~the distance from the previous/next {\thething}, the distance from the start/end of the series, etc.
\end{enumerate}
Following this process allows the release, and thereafter processing, of {\thething} timestamps.
Thus, we provide an extra layer of privacy protection when we separate {\thethings} from regular events.
One approach would be to utilize the randomized response (described in detail in Section~\ref{subsec:prv-mech}) and randomize the answer to the question \emph{`Is the current event a {\thething}?'} for every timestamp in $T \supseteq L$ of the time series $S_T$.
However, this could result in a new {\thething} set $L'$ that does not include all (or even any) of the timestamps in $L$.
This contradicts the main idea of {\thething} privacy, i.e.,~take into account all {\thethings} at every timestamp.