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correlation: Minor corrections

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Manos Katsomallos
2021-08-02 23:15:56 +03:00
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text/preliminaries/correlation.tex
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@ -1,8 +1,8 @@
\section{Data correlation} \section{Data correlation}
\label{sec:correlation} \label{sec:correlation}
\subsection{Types of correlation} \subsection{Types of correlation}
\label{subsec:cor-types}
The most prominent types of correlation might be: The most prominent types of correlation might be:
@ -18,6 +18,7 @@ A positive spatial autocorrelation indicates that similar data are \emph{cluster
\subsection{Extraction of correlation} \subsection{Extraction of correlation}
\label{subsec:cor-ext}
A common practice for extracting data dependence from continuous data, is by expressing the data as a \emph{stochastic} or \emph{random process}. A common practice for extracting data dependence from continuous data, is by expressing the data as a \emph{stochastic} or \emph{random process}.
A random process is a collection of \emph{random variables} or \emph{bivariate data}, indexed by some set, e.g.,~a series of timestamps, a Cartesian plane $\mathbb{R}^2$, an $n$-dimensional Euclidean space, etc.~\cite{skorokhod2005basic}. A random process is a collection of \emph{random variables} or \emph{bivariate data}, indexed by some set, e.g.,~a series of timestamps, a Cartesian plane $\mathbb{R}^2$, an $n$-dimensional Euclidean space, etc.~\cite{skorokhod2005basic}.
@ -38,6 +39,7 @@ Some common stochastic processes modeling techniques include:
\subsection{Privacy risks of correlation} \subsection{Privacy risks of correlation}
\label{subsec:cor-prv}
Correlation appears in dependent data: Correlation appears in dependent data:
@ -60,6 +62,7 @@ A positive correlation indicates that the variables behave in a \emph{similar} m
\subsection{Privacy loss under temporal correlation} \subsection{Privacy loss under temporal correlation}
\label{subsec:cor-temp}
% The presence of temporal correlation might result into additional privacy loss consisting of \emph{backward privacy loss} $\alpha^B$ and \emph{forward privacy loss} $\alpha^F$~\cite{cao2017quantifying}. % The presence of temporal correlation might result into additional privacy loss consisting of \emph{backward privacy loss} $\alpha^B$ and \emph{forward privacy loss} $\alpha^F$~\cite{cao2017quantifying}.
Cao et al.~\cite{cao2017quantifying} propose a method for computing the temporal privacy loss (TPL) of a differential privacy mechanism in the presence of temporal correlation and background knowledge. Cao et al.~\cite{cao2017quantifying} propose a method for computing the temporal privacy loss (TPL) of a differential privacy mechanism in the presence of temporal correlation and background knowledge.