From bf5b05a84e877391fddd1b0a0b752f71ec05e901 Mon Sep 17 00:00:00 2001
From: Jan Aalmoes <jan.aalmoes@inria.fr>
Date: Wed, 11 Sep 2024 00:10:50 +0200
Subject: Preuve existe f pas cca equivalant exists f BA pas randomguess

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+In this section we analyse the impact of using syhthetic data instead of real data on MIA and AIA.
+Section~\ref{sec:uti} presents the utilisy of the target. 
+This control factor allows us to assess that every model has learned some level of information and is not random guessing the label.
+
+\subsection{Utility}
+\label{sec:uti}
+
+\begin{figure}
+    \centering
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/utility.pdf}
+        \caption{Adult}
+    \end{subfigure}
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/utility.pdf}
+        \caption{CelebA}
+    \end{subfigure}
+    \caption{Utility of the target model in terms of balanced accuracy evaluated on unseen data.
+    The "Real" label refers to a generator equal to identity, hence the synthetic data used to train the target model is the real data.
+    THe "Synthetic" label refers to a CGAN generator for Adult and CTGAN for CelebA, hence the synthetic data are generated sampled according to a distribution learned by the genrator model. 
+    In this case the target model is not trained on real date.}
+\end{figure}
+Using synthetic datatset degrades the utility of the predictor.
+
+\subsection{Membership inference attack}
+\begin{figure}
+    \centering
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/mia.pdf}
+        \caption{Adult}
+    \end{subfigure}
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/mia.pdf}
+        \caption{CelebA}
+    \end{subfigure}
+    \caption{Success of the MIA in terms of balanced accuracy evaluated on the Train part of MIA dataset.}
+\end{figure}
+Using synthetic dataset slightly degrades the success of membership inference attack.
+
+\subsection{Attribute inference attack}
+\begin{figure}
+    \centering
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/aia.pdf}
+        \caption{Adult}
+    \end{subfigure}
+    \begin{subfigure}{0.45\linewidth}
+    \includegraphics[width=\textwidth]{synthetic/figure/result/adult/aia.pdf}
+        \caption{CelebA}
+    \end{subfigure}
+    \caption{Success of the AIA in terms of balanced accuracy evaluated on the Train part of AIA dataset.}
+\end{figure}
+Using synthetic dataset does not have an impact on the success of attrivute inference atttack.
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