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Adding first remakrs

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Louis 2025-05-27 14:39:53 +02:00
parent 7d6b420a26
commit c951d28e35
2 changed files with 8 additions and 8 deletions
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12
annexe.tex
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@ -86,10 +86,10 @@
\item BIC-L = ICLv mais sans la pénalité sur l'entropie et la rajoutant à la fin \item BIC-L = ICLv mais sans la pénalité sur l'entropie et la rajoutant à la fin
\end{itemize} \end{itemize}
\begin{align*} \begin{align*}
\text{BIC}(\hat{\theta}) & = \log p(\mathbf{Y};\hat{\theta}) - \frac{1}{2} \text{pen}(\dots) \\ \text{BIC}(\hat{\theta}) & = \log p(\mathbf{Y};\hat{\theta}) - \frac{1}{2} \text{pen}(\dots) \\
& = \Esp_{\mathbf{Z}, \mathbf{W}|\mathbf{Y}} [\log p(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta})] + \mathcal{H}(p(\mathbf{Z},\mathbf{W}|\mathbf{Y})) - \frac{1}{2} \text{pen}(\dots) \\ & = \Esp_{\mathbf{Z}, \mathbf{W}|\mathbf{Y}} [\underbrace{\log p(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta})}_{\ell_c(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta})}] + \mathcal{H}(p(\mathbf{Z},\mathbf{W}|\mathbf{Y})) - \frac{1}{2} \text{pen}(\dots) \\
\text{ICL}(\hat{\theta}) & = \Esp_{\mathbf{Z}, \mathbf{W}|\mathbf{Y}} [\ell_c(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta})] - \frac{1}{2} \text{pen}(\dots) \\ \text{ICL}(\hat{\theta}) & = \Esp_{\mathbf{Z}, \mathbf{W}|\mathbf{Y}} [\ell_c(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta})] - \frac{1}{2} \text{pen}(\dots) \\
\text{BIC-L}(\hat{\theta}, \hat{\tau}) & = \Esp_{\mathcal{R}_{\mathbf{Y}, \hat{\tau}}}[\ell_c(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta}^{\text{var}})] + \mathcal{H}(\mathcal{R}_{\mathbf{Y}, \hat{\tau}}) - \frac{1}{2} \text{pen}(\dots) \\ \text{BIC-L}(\hat{\theta}, \hat{\tau}) & = \Esp_{\mathcal{R}_{\mathbf{Y}, \hat{\tau}}}[\ell_c(\mathbf{Y},\mathbf{Z},\mathbf{W};\hat{\theta}^{\text{var}})] + \mathcal{H}(\mathcal{R}_{\mathbf{Y}, \hat{\tau}}) - \frac{1}{2} \text{pen}(\dots) \\
\end{align*} \end{align*}
\end{frame} \end{frame}
@ -105,7 +105,7 @@
\end{column} \end{column}
\begin{column}{0.35\linewidth} \begin{column}{0.35\linewidth}
\begin{itemize} \begin{itemize}
\item Initial model~:\\ \item Initial model~: \\ \vspace{0.125\baselineskip}
\begin{tikzpicture} \begin{tikzpicture}
\draw[fill=gray, draw=gray] circle [radius=0.225cm]; \draw[fill=gray, draw=gray] circle [radius=0.225cm];
\end{tikzpicture} \end{tikzpicture}
@ -114,7 +114,7 @@
\begin{tikzpicture} \begin{tikzpicture}
\draw[fill=blueind, draw=blueind] circle [radius=0.225cm]; \draw[fill=blueind, draw=blueind] circle [radius=0.225cm];
\end{tikzpicture} \end{tikzpicture}
\item Model maximizing the criterion~:\\ \item Model maximizing the criterion~:\\ \vspace{0.125\baselineskip}
\begin{tikzpicture} \begin{tikzpicture}
\draw[fill=white, draw=green, very thick] circle [radius=0.225cm]; \draw[fill=white, draw=green, very thick] circle [radius=0.225cm];
\end{tikzpicture} \end{tikzpicture}

4
principal.tex
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@ -414,7 +414,7 @@
\path (towns_spe_red) edge[->,thick] (spe); \path (towns_spe_red) edge[->,thick] (spe);
} }
\end{tikzpicture} \end{tikzpicture}
\caption{Shared structure of the 4 networks}\label{fig:shared} \caption{Shared structure ($\alpha$ matrix) of the four networks}\label{fig:shared}
\end{figure} \end{figure}
\end{column} \end{column}
\end{columns} \end{columns}
@ -431,7 +431,7 @@
\centering \centering
\includegraphics[scale=0.1]{backup-app-iid-struct1.png} \includegraphics[scale=0.1]{backup-app-iid-struct1.png}
\includegraphics[scale=0.2]{backup-app-iid-struct2.png} \includegraphics[scale=0.2]{backup-app-iid-struct2.png}
\caption{Model $iid$, separate African (left) and English (right) networks} \caption{Model $iid$, separate Kenyan (left) and British (right) networks}
\end{figure} \end{figure}
\end{frame} \end{frame}
\begin{frame} \begin{frame}