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.