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lmdk-eval: Sectioning

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% \kat{After discussing with Dimitris, I thought you are keeping one chapter for the proposals of the thesis. In this case, it would be more clean to keep the theoretical contributions in one chapter and the evaluation in a separate chapter. } % \kat{After discussing with Dimitris, I thought you are keeping one chapter for the proposals of the thesis. In this case, it would be more clean to keep the theoretical contributions in one chapter and the evaluation in a separate chapter. }
% \mk{OK.} % \mk{OK.}
In this section we present the experiments that we performed on real and synthetic data sets. In this section we present the experiments that we performed on real and synthetic data sets.
With the experiments on the synthetic data sets we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$. With the experiments on the real data sets (Section~\ref{subsec:lmdk-expt-bgt}), we show the performance in terms of utility of our three {\thething} mechanisms.
We also show how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}. With the experiments on the synthetic data sets (Section~\ref{subsec:lmdk-expt-cor}) we show the privacy loss by our framework when tuning the size and statistical characteristics of the input {\thething} set $L$ with special emphasis on how the privacy loss under temporal correlation is affected by the number and distribution of the {\thethings}.
With the experiments on the real data sets, we show the performance in terms of utility of our three {\thething} mechanisms.
Notice that in our experiments, in the cases when we have $0\%$ and $100\%$ of the events being {\thethings}, we get the same behavior as in event- and user-level privacy respectively. Notice that in our experiments, in the cases when we have $0\%$ and $100\%$ of the events being {\thethings}, we get the same behavior as in event- and user-level privacy respectively.
This happens due the fact that at each timestamp we take into account only the data items at the current timestamp and ignore the rest of the time series (event-level) when there are no {\thethings}. This happens due the fact that at each timestamp we take into account only the data items at the current timestamp and ignore the rest of the time series (event-level) when there are no {\thethings}.
Whereas, when each timestamp corresponds to a {\thething} we consider and protect all the events throughout the entire series (user-level). Whereas, when each timestamp corresponds to a {\thething} we consider and protect all the events throughout the entire series (user-level).
\subsection{Experiments} \subsection{Budget allocation schemes}
\label{sec:lmdk-expt} \label{subsec:lmdk-expt-bgt}
\subsubsection{Budget allocation schemes}
Figure~\ref{fig:real} exhibits the performance of the three mechanisms: Skip, Uniform, and Adaptive. Figure~\ref{fig:real} exhibits the performance of the three mechanisms: Skip, Uniform, and Adaptive.
@ -51,7 +49,8 @@ In general, we can claim that the Adaptive is the most reliable and best perform
Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive. Moreover, designing a data-dependent sampling scheme would possibly result in better results for Adaptive.
\subsubsection{Temporal distance and correlation} \subsection{Temporal distance and correlation}
\label{subsec:lmdk-expt-cor}
Figure~\ref{fig:avg-dist} shows a comparison of the average temporal distance of the events from the previous/next {\thething} or the start/end of the time series for various distributions in synthetic data. Figure~\ref{fig:avg-dist} shows a comparison of the average temporal distance of the events from the previous/next {\thething} or the start/end of the time series for various distributions in synthetic data.
More particularly, we count for every event the total number of events between itself and the nearest {\thething} or the series edge. More particularly, we count for every event the total number of events between itself and the nearest {\thething} or the series edge.