diff --git a/text/evaluation/details.tex b/text/evaluation/details.tex index ce04e30..2eca13b 100644 --- a/text/evaluation/details.tex +++ b/text/evaluation/details.tex @@ -38,7 +38,6 @@ We sampled the first $1000$ data items of the taxi with identifier `$2$'. \subsubsection{Synthetic} We generated synthetic time series of length equal to $100$ timestamps, for which we varied the number and distribution of {\thethings}. We take into account only the temporal order of the points and the position of regular and {\thething} events within the series. -% Note, that for the experiments performed on the synthetic data sets, the original values to be released do not influence the outcome of our conclusions, thus we ignore them. \subsection{Configurations} @@ -46,7 +45,7 @@ We take into account only the temporal order of the points and the position of r \subsubsection{{\Thethings}' percentage} -For Copenhagen, we achieve +For the Copenhagen data set, we achieve $0\%$ {\thethings} by considering an empty list of contact devices, $20\%$ by extending the list with $[3$, $6$, $11$, $12$, $25$, $29$, $36$, $39$, $41$, $46$, $47$, $50$, $52$, $56$, $57$, $61$, $63$, $78$, $80]$, $40\%$ with $[81$, $88$, $90$, $97$, $101$, $128$, $130$, $131$, $137$, $145$, $146$, $148$, $151$, $158$, $166$, $175$, $176]$, @@ -88,9 +87,10 @@ In our experiments, for simplicity, we set $n = 2$ and we investigate the effect \subsubsection{Privacy parameters} -To perturb the contact tracing data of Copenhagen, we utilize the \emph{random response} technique to report with probability $p = \frac{e^\varepsilon}{e^\varepsilon + 1}$ weather the current contact is a {\thething} or not. -We randomize them the energy consumption in HUE with the Laplace mechanism. +To perturb the contact tracing data of the Copenhagen data set, we utilize the \emph{random response} technique~\cite{wang2017locally} to report with probability $p = \frac{e^\varepsilon}{e^\varepsilon + 1}$ whether the current contact is a {\thething} or not. +We randomize the energy consumption in HUE with the Laplace mechanism (described in detail in Section~\ref{subsec:prv-mech}). To perturb the spatial values in T-drive, we inject noise that we sample from the Planar Laplace mechanism~\cite{andres2013geo}. We set the privacy budget $\varepsilon = 1$, and, for simplicity, we assume that for every query sensitivity it holds that $\Delta f = 1$. +For the experiments performed on the synthetic data sets, the original values to be released do not influence the outcome of our conclusions, thus we ignore them. % Finally, notice that, depending on the results' variation, most diagrams are in logarithmic scale. diff --git a/text/preliminaries/privacy.tex b/text/preliminaries/privacy.tex index 033231e..9259948 100644 --- a/text/preliminaries/privacy.tex +++ b/text/preliminaries/privacy.tex @@ -291,8 +291,8 @@ queries can be problematic, since a single, outlier value could change the outpu \paragraph{Popular privacy mechanisms} - \label{subsec:prv-mech} + A typical example of a differential privacy mechanism is the \emph{Laplace mechanism}~\cite{dwork2014algorithmic}. It draws randomly a value from the probability distribution of $\textrm{Laplace}(\mu, b)$, where $\mu$ stands for the location parameter and $b > 0$ is the scale parameter (Figure~\ref{fig:laplace}). In our case, $\mu$ is equal to the original output value of a query function, and $b$ is the sensitivity of the query function divided by $\varepsilon$.