rapport : various updates

rapport/chapter2-context.tex

@@ -137,7 +137,8 @@ On \ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong
 to the row block of corresponding color, $\bm{\rho}$ are the probabilities for
 a column node to belong to the column block of corresponding color and
 $\bm{\alpha}$ is a matrix $Q_1 \times Q_2$ of the connectivity parameters
-between the row and column blocks.
+between the row and column blocks. When we talk about the \enquote{structure}
+of the network we are referring to this connectivity matrix.
 
 This model can be used to easily generate bipartite graphs with complex and
 very varied structures. But when trying to determine the structure of a given

rapport/chapter3-structure-detection.tex

@@ -15,9 +15,10 @@ BiSBM for each network of the collection.
 
 For network $m$, let $n_1^m$ (resp. $n_2^m$) be the number of nodes in row
 (resp. column) divided into $Q_1^m$ row clusters (resp. $Q_2^m$ column
-clusters).\\ Let $Z^m~=~(Z^m_i, \dots, Z^m_{n_1^m})$ and $W^m~=~(W^m_j, \dots,
-    W^m_{n_2^m})$ be independent latent variables such that $Z^m_i = q$ if row node
-$i$ of network $m$ belongs to row cluster $q$ ($q\in\{1,\dots,Q_1^m\}$) and
+clusters).\\ Let $Z^m=(Z^m_1, \dots, Z^m_i, \dots, Z^m_{n_1^m})$ and
+$W^m = (W^m_1, \dots,W^m_j, \dots, W^m_{n_2^m})$ be independent latent variables
+such that $Z^m_i = q$ if row node $i$ of network $m$ belongs to row cluster $q$
+($q\in\{1,\dots,Q_1^m\}$) and
 $W^m_j = r$ if column node $j$ of network $m$ belong to column block $r$
 ($r\in\{1,\dots,Q_2^m\}$). And we have
 \begin{align}\label{eqn:lbm-block-membership-prob}
@@ -749,3 +750,10 @@ $G_1$ and $G_2$. Else we return $\mathcal{G}$.
 
 We illustrate our capacity to perform a partition of a collection for all
 colBiSBM models in %\ref{sec:network-clustering-of-simulated-networks}.
+
+\section{Model identifiability}
+\label{sec:model-identifiability}
+
+% Ici l'identifiabilité du modèle
+
+\cite{chabert-liddellLearningCommonStructures2024a,celisseConsistencyMaximumlikelihoodVariational2012,keribinEstimationSelectionLatent2015}

rapport/chapter4-simulation-studies.tex

@@ -7,7 +7,7 @@ performances and the clustering capacities.
 
 \paragraph{Reproducibility} All the codes used to obtain data and to perform the analysis can be found on
 the report repository at
-\url{https://gitea.polarolouis.fr/polarolouis/rapport-CEI-MIA-2023}.
+\url{https://gitea.polarolouis.fr/polarolouis/mia-stage-2024}.
 
 
 \input{chapter4-simulations/inference}

rapport/conclusions.tex

@@ -0,0 +1,3 @@
+\addtocounter{customchapter}{1}
+\chapter{Conclusions and future work}
+\label{chap:conclusions-and-future-work}

rapport/rapport.tex

@@ -211,29 +211,31 @@ automata,positioning}
 % Pour activer les onglets
 \ActivateBG
 \begin{selectlanguage}{french}
-    % \maketitle
-    \pagenumbering{roman}
-    \tableofcontents
-    \include{remerciements}
-    % \include{chapter1-presentation_UMR}
+	% \maketitle
+	\pagenumbering{roman}
+	\tableofcontents
+	\include{remerciements}
+	% \include{chapter1-presentation_UMR}
 \end{selectlanguage}
 
 \begin{selectlanguage}{english}
-    \pagenumbering{arabic}
-    \include{chapter2-context}
-    \include{chapter3-structure-detection}
-    \include{chapter4-simulation-studies}
+	\pagenumbering{arabic}
+	\include{chapter2-context}
+	\include{chapter3-structure-detection}
+	\include{chapter4-simulation-studies}
 
-    % \chapter{Applications}
-    % \include{Rcodes/real_data/application_dore}
-    % \include{Rcodes/real_data/CoOPLBM_completion_analyze}
+	% \chapter{Applications}
+	% \include{Rcodes/real_data/application_dore}
+	% \include{Rcodes/real_data/CoOPLBM_completion_analyze}
 
-    \addtocounter{maincontentend}{1}
-    \addtocounter{customchapter}{1}
-    \printbibliography
-    \input{appendices.tex}
-    % \listoffigures
-    % \listoftables
+	\include{conclusions}
+
+	\addtocounter{maincontentend}{1}
+	\addtocounter{customchapter}{1}
+	\printbibliography
+	\input{appendices.tex}
+	% \listoffigures
+	% \listoftables
 \end{selectlanguage}
 
 \end{document}

rapport/remerciements.tex

@@ -13,9 +13,11 @@ Merci à Farida, Christelle et Sébastien pour avoir expliqué et mené les
 démarches administratives.
 
 Un merci tout particulier à tous les doctorants : Mary,
-Marina, Emré, Tam, Caroline, Jérémy, Florian, Annaïg, Jules, Hayato, Tanguy, Barbara,
+Marina, Emré, Tam, Caroline, Jérémy, Florian, Annaïg, Jules, Hayato, Jeanne,
+Tanguy, Barbara,
 Bastien et Armand. Merci à tous les autres stagiaires, particulièrement:
-Alizée, Taliesin, Antoine, Alexandre, Francois, Pierre, Camille et Maxime.
+Alizée, Taliesin, Antoine, Alexandre, Francois, Vincent, Pierre, Camille et
+Maxime.
 
 Merci à tous les permanents du 3\ieme étage, parmi lesquels: Christophe,
 Stéphane et Vincent.