From c951d28e35d485764b3a364199cb110bd41ab626 Mon Sep 17 00:00:00 2001
From: Louis <louis.lacoste@agroparistech.fr>
Date: Tue, 27 May 2025 14:39:53 +0200
Subject: [PATCH] Adding first remakrs

---
 annexe.tex    | 12 ++++++------
 principal.tex |  4 ++--
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/annexe.tex b/annexe.tex
index a53c593..a73576a 100644
--- a/annexe.tex
+++ b/annexe.tex
@@ -86,10 +86,10 @@
         \item BIC-L = ICLv mais sans la pénalité sur l'entropie et la rajoutant à la fin
     \end{itemize}
     \begin{align*}
-        \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)                 \\
-        \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}(\hat{\theta})               & = \log p(\mathbf{Y};\hat{\theta}) - \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{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{frame}
 
@@ -105,7 +105,7 @@
         \end{column}
         \begin{column}{0.35\linewidth}
             \begin{itemize}
-                \item Initial model~:\\
+                \item Initial model~: \\ \vspace{0.125\baselineskip}
                       \begin{tikzpicture}
                           \draw[fill=gray, draw=gray] circle [radius=0.225cm];
                       \end{tikzpicture}
@@ -114,7 +114,7 @@
                       \begin{tikzpicture}
                           \draw[fill=blueind, draw=blueind] circle [radius=0.225cm];
                       \end{tikzpicture}
-                \item Model maximizing the criterion~:\\
+                \item Model maximizing the criterion~:\\ \vspace{0.125\baselineskip}
                       \begin{tikzpicture}
                           \draw[fill=white, draw=green, very thick] circle [radius=0.225cm];
                       \end{tikzpicture}
diff --git a/principal.tex b/principal.tex
index 95dad86..153408a 100644
--- a/principal.tex
+++ b/principal.tex
@@ -414,7 +414,7 @@
                             \path (towns_spe_red) edge[->,thick] (spe);
                         }
                     \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{column}
         \end{columns}
@@ -431,7 +431,7 @@
         \centering
         \includegraphics[scale=0.1]{backup-app-iid-struct1.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{frame}
 \begin{frame}