51 lines
4.9 KiB
TeX
51 lines
4.9 KiB
TeX
\section{Significant events}
|
|
\label{sec:thething}
|
|
|
|
The privacy mechanisms for the aforementioned levels assume that in a time series any single event, or any sequence of events, or the entire series of events is equally privacy-significant for the users.
|
|
In reality, this is an simplistic assumption.
|
|
The significance of an event is related to certain user-defined privacy criteria, or to its adjacent events, as well as to the entire time series.
|
|
We term significant events as \emph{{\thething} events} or simply \emph{\thethings}.
|
|
Identifying {\thethings} can be done in an automatic or manual way (but is out of scope for this work).
|
|
For example, in spatiotemporal data, \emph{places where an individual spent some time} denote \emph{points of interest} (POIs) (called also stay points)~\cite{zheng2015trajectory}.
|
|
Such events, and more particularly their spatial attribute values, can be less privacy-sensitive~\cite{primault2018long}, e.g.,~parks, theaters, etc. or, if individuals frequent them, they can reveal supplementary information, e.g.,~residences (home addresses)~\cite{gambs2010show}, places of worship (religious beliefs)~\cite{franceschi-bicchierairussell2015redditor}, etc.
|
|
POIs can be an example of how we can choose {\thethings}, but the idea is not limited to these.
|
|
Another example is the detection of privacy-sensitive user interactions by \emph{contact tracing} applications.
|
|
This can be practical in decease control~\cite{eames2003contact}, similar to the recent outbreak of the Coronavirus disease 2019 (COVID-19) epidemic~\cite{ahmed2020survey}.
|
|
Last but not least, {\thethings} in \emph{smart grid} electricity usage patterns could not only reveal the energy consumption of a user but also information regarding activities, e.g.,~`at work', `sleeping', etc. and types of appliances already installed or recently purchased~\cite{khurana2010smart}.
|
|
|
|
\begin{example}
|
|
\label{ex:st-cont}
|
|
|
|
Figure~\ref{fig:st-cont} shows the case when we want to protect all of Bob's significant events ($p_1$, $p_3$, $p_5$, $p_8$) in his trajectory shown in Figure~\ref{fig:scenario}.
|
|
% That is, we have to allocate privacy budget $\varepsilon$ such that at any timestamp $t$ it holds that $\varepsilon_t + \varepsilon_1 + \varepsilon_3 + \varepsilon_5 + \varepsilon_8 \leq \varepsilon$.
|
|
In this scenario, event-level protection is not suitable since it can only protect one event at a time.
|
|
Hence, we have to apply user-level privacy protection by distributing equal portions of $\varepsilon$ to all the events, i.e.,~$\frac{\varepsilon}{8}$ to each one (the equivalent of applying $8$-event privacy).
|
|
In this way, we have protected the {\thething} points; we have allocated a total of $\frac{\varepsilon}{2}<\varepsilon$ to the {\thethings}.
|
|
|
|
\begin{figure}[htp]
|
|
\centering
|
|
\includegraphics[width=\linewidth]{problem/st-cont}
|
|
\caption{User-level and {\thething} $\varepsilon$-differential privacy protection for the time series of Figure~\ref{fig:scenario}.}
|
|
\label{fig:st-cont}
|
|
\end{figure}
|
|
|
|
However, perturbing by $\frac{\varepsilon}{8}$ each regular point deteriorates the data utility unnecessarily.
|
|
Notice that the overall privacy budget that we ended up allocating to the user-defined significant events is equal to $\frac{\varepsilon}{2}$ and leaves an equal amount of budget to distribute to any current event.
|
|
In other words, uniformly allocating $\frac{\varepsilon}{5}$ to every event would still achieve the Bob's privacy goal, i.e.,~protect every significant event, while achieving better utility overall.
|
|
|
|
\end{example}
|
|
|
|
We argue that protecting only {\thething} events along with any regular event release is sufficient for the user's protection, while it improves data utility.
|
|
Considering {\thething} events can prevent over-perturbing the data in the benefit of their final quality.
|
|
Take for example the scenario in Figure~\ref{fig:st-cont}, where {\thethings} are highlighted in gray.
|
|
If we want to protect the {\thething} points, we have to allocate at most a budget of $\varepsilon$ to the {\thethings}, while saving some for the release of regular events.
|
|
Essentially, the more budget we allocate to an event the less we protect it, but at the same time we maintain its utility.
|
|
With {\thething} privacy we propose to distribute the budget taking into account only the existence of the {\thethings} when we release an event of the time series, i.e.,~allocating $\frac{\varepsilon}{5}$ ($4\ \text{\thethings} + 1\ \text{regular point}$) to each event (see Figure~\ref{fig:st-cont}).
|
|
This way, we still guarantee that the {\thethings} are adequately protected, as they receive a total budget of $\frac{4\varepsilon}{5}<\varepsilon$.
|
|
At the same time, we avoid over-perturbing the regular events, as we allocate to them a higher total budget ($\frac{4\varepsilon}{5}$) than in user-level ($\frac{\varepsilon}{2}$), and thus less noise.
|
|
|
|
|
|
\input{problem/thething/contribution}
|
|
\input{problem/thething/problem}
|
|
\input{problem/thething/solution}
|