Adding translation in english
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9 changed files with 151 additions and 150 deletions
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@ -24,6 +24,8 @@
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## Generated if empty string is given at "Please type another file name for output:"
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.pdf
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*.pdf
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## Bibliography auxiliary files (bibtex/biblatex/biber):
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*.bbl
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*.bbl-SAVE-ERROR
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12
annexe.tex
12
annexe.tex
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@ -1,7 +1,7 @@
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\section{VEM}
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\begin{frame}
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\frametitle{Pourquoi VE minimise KL ?}
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\frametitle{Why does VE minimizes KL ?}
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\begin{align*}
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\ell_c(\bY,\bZ,\bW;\theta) & = \log \Prob(\bZ, \bW|\bY;\theta) + \ell(\bY;\theta) \\
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\Leftrightarrow \ell(\bY;\theta) & = \ell_c(\bY,\bZ,\bW;\theta) - \log \Prob(\bZ, \bW|\bY;\theta) \\
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@ -9,14 +9,14 @@
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\Leftrightarrow \ell(\bY;\theta) & = \Esp_{\Ryt}[\ell_c(\bY,\bZ,\bW;\theta)] - \Esp_{\Ryt}[\log \Prob(\bZ,\bW|\bY;\theta)] \\
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\end{align*}
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\begin{align*}
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\text{Or }\KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} & = - \Esp_{\Ryt} [\log \frac{\Prob(\bZ,\bW|\bY;\theta)}{\Ryt}] \\
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\text{But }\KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} & = - \Esp_{\Ryt} [\log \frac{\Prob(\bZ,\bW|\bY;\theta)}{\Ryt}] \\
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= - \Esp_{\Ryt} [\log \Prob(\bZ,\bW|\bY;\theta)] + & \underbrace{\Esp_{\Ryt[\log \Ryt]}}_{-\Hshannon(\Ryt)} \\
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\Leftrightarrow \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} + \Hshannon(\Ryt) & = - \Esp_{\Ryt} [\log \Prob(\bZ,\bW|\bY;\theta)]
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\end{align*}
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D'où $\ell(\bY;\theta) - \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} = \mathcal{J}(\tau;\theta) \qed$
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Thus $\ell(\bY;\theta) - \KL{\Ryt}{\log \Prob(\bZ,\bW|\bY;\theta)} = \mathcal{J}(\tau;\theta) \qed$
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\end{frame}
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\section{Résultats~\cite{baldockSystemsApproachReveals2019a,baldockDailyTemporalStructure2011}}
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\section{Résultats~\cite{baldockSystemsApproachReveals2019,baldockDailyTemporalStructure2011}}
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\begin{frame}[allowframebreaks]
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\begin{figure}[ht]
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\centering
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@ -28,7 +28,7 @@
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\begin{subfigure}[t]{0.5\textwidth}
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\centering
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\includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol.pdf}
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\caption{Réordonnée}
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\caption{Reordered}
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\end{subfigure}
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\caption{Bristol}
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\end{figure}
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@ -43,7 +43,7 @@
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\begin{subfigure}[t]{0.5\textwidth}
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\centering
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\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh.pdf}
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\caption{Réordonnée}
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\caption{Reordered}
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\end{subfigure}
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\caption{Edinburgh}
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\end{figure}
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@ -2,7 +2,7 @@
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\usetheme{Boadilla}
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% importations
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\usepackage[french]{babel} % pour dire que le texte est en francais
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% \usepackage[french]{babel} % pour dire que le texte est en francais
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\usepackage{csquotes}
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\usepackage[T1]{fontenc} % pour les font postscript
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\usepackage[cyr]{aeguill} % Police vectorielle TrueType, guillemets francais
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@ -111,9 +111,8 @@
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\subtitle{Présentation LSD}
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\title[Collections de réseaux bipartites]{Analyse jointe de collections de
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réseaux bipartites}
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\author[L. Lacoste]{Louis \textsc{Lacoste}, encadré par Pierre Barbillon et
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\title[Bipartite networks collection]{Joint analysis of bipartite networks collection}
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\author[L. Lacoste]{Louis \textsc{Lacoste}, under the supervision of Pierre Barbillon and
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Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pierre
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\date{}
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@ -129,7 +128,7 @@ Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pie
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\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}}
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\begin{frame}[noframenumbering,plain,allowframebreaks]
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\frametitle{Bibliographie}
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\frametitle{References}
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\printbibliography
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\end{frame}
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\end{refsection}
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@ -139,9 +138,9 @@ Sophie Donnet\newline Laboratoire MIA Paris-Saclay} % Sous la supervision de Pie
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\begin{refsection}
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\include{annexe}
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\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}}
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\section{Références annexes}
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\section{Appendices references}
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\begin{frame}[noframenumbering,plain,allowframebreaks]
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\frametitle{Bibliographie des annexes}
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\frametitle{Appendices references}
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\printbibliography
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\end{frame}
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\end{refsection}
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274
principal.tex
274
principal.tex
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@ -1,8 +1,8 @@
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\section{Contexte du modèle}
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\label{sec:contexte-du-modele}
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\section{Model Context}
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\label{sec:context-of-the-model}
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\begin{frame}
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\frametitle{Pourquoi un réseau ?}
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\frametitle{Why a network?}
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\begin{columns}
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\begin{column}{0.5\textwidth}
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\begin{columns}
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@ -12,8 +12,8 @@
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\begin{tikzpicture}[scale=.6,rotate=270]
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\input{tikz/plantpollinatornetwork.tex}
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\end{tikzpicture}
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\caption{Exemple d'un réseau}
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\label{fig:plantes-pollin}
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\caption{Example of a network}
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\label{fig:plants-pollin}
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\end{figure}
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\end{column}
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\begin{column}{0.3\textwidth}
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@ -27,34 +27,34 @@
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\end{pmatrix}
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\end{align*}
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\footnotesize
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Matrice d'adjacence associée
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Associated adjacency matrix
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\end{column}
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\end{columns}
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\begin{figure}[ht]
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\centering
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\includestandalone[width=0.7\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol}
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\caption{Réseau plante-pollinisateur de
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Bristol\newline\cite{baldockSystemsApproachReveals2019a}}
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\includegraphics[width=0.7\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol.pdf}
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\caption{Plant-pollinator network of
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Bristol\newline\cite{baldockSystemsApproachReveals2019}}
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\label{fig:label}
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\end{figure}
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\end{column}
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\begin{column}{0.5\textwidth}
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\begin{itemize}
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\item Modélisation d'interactions variées, ici d'écosystèmes
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\item Structure nécessaire pour~: suivi biodiversité, robustesse, risque
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d'effondrement
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\item De plus en plus disponibles
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\item Modeling of various interactions, here ecosystems
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\item Structure necessary for: biodiversity monitoring, robustness, risk
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of collapse
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\item Increasingly available
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\end{itemize}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Méthodes d'analyse pour un réseau}
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Plusieurs méthodes~:
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\begin{frame}{Analysis methods for a network}
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Several methods~:
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\begin{itemize}
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\item Métriques~: degré, centralité, emboîtement \dots
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\item Plongement des réseaux avec GNN
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\item \textbf<2>{\emph{Clustering} des n\oe uds avec modèles à variables latentes}
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\item Metrics~: degree, centrality, nesting \dots
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\item Network embedding with GNN
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\item \textbf<2>{\emph{Clustering} of nodes with latent variable models}
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\end{itemize}
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\end{frame}
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\begin{tikzpicture}[scale=0.35]
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\input{tikz/lbm.tex}
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\end{tikzpicture}
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\caption{Exemple de LBM\footnotemark[\thefootnote]}
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\caption{Example of LBM\footnotemark[\thefootnote]}
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\label{fig:LBMvisu}
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\end{figure}
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\end{column}
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\only<1>{
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\begin{column}{0.51\linewidth}
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\begin{block}{Modèle hiérarchique}
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\begin{block}{Hierarchical model}
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\vspace{-\baselineskip}
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\begin{align*}
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\forall q\in[\![ 1, Q_1]\!],~ & \mathbb{P}(Z_i = q) = \pi_q \\
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\forall r\in[\![ 1, Q_2]\!],~ & \mathbb{P}(W_j = r) = \rho_r \\
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& Y_{ij} | Z_i, W_j \sim \mathcal{F}(\alpha_{Z_i,W_j})
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\end{align*}
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où $|\pi| = Q_1, |\rho| = Q_2, |\alpha| = Q_1 \times Q_2$
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where $|\pi| = Q_1, |\rho| = Q_2, |\alpha| = Q_1 \times Q_2$
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\end{block}
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\begin{block}{Formule concise LBM}
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\begin{block}{Concise LBM formula}
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$Y \sim \mathcal{F}\text{-BiSBM}_{n_1,n_2}(Q_1, Q_2, \pi, \rho, \alpha)$
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\end{block}
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\end{column}}
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\only<2>{
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\begin{column}{0.51\linewidth}
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Avec \begin{itemize}
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\item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ blocs fixés en ligne
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\item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ blocs fixés en colonne
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With \begin{itemize}
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\item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ fixed row blocks
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\item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ fixed column blocks
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\end{itemize}
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\begin{block}{Paramètres}
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\begin{block}{Parameters}
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\begin{itemize}
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\item $\pi_{{\color{blueind}\bullet}} = \mathbb{P}(Z_i = {\color{blueind}\bullet})$
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\item $\rho_{{\color{burntorange}\bullet}} = \mathbb{P}(W_j = {\color{burntorange}\bullet})$
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@ -105,11 +105,11 @@
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\end{column}}
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\end{columns}
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\footnotetext[\thefootnote]{Que j'appellerai par la suite BiSBM}
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\footnotetext[\thefootnote]{Which I will henceforth call BiSBM}
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\end{frame}
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\begin{frame}
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\frametitle{Plusieurs réseaux}
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\frametitle{Multiple networks}
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\begin{figure}[ht]
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\centering
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\begin{subfigure}[ht]{0.3\textwidth}
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@ -124,15 +124,15 @@
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\includegraphics[width=1.1\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds.pdf}
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\caption{Leeds}
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\end{subfigure}
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\caption{Matrices d'adjacence,~\cite{baldockSystemsApproachReveals2019a}}
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\caption{Adjacency matrices,~\cite{baldockSystemsApproachReveals2019}}
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\label{fig:adj}
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\end{figure}
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\end{frame}
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\section[Modèles collection bipartites]{Modèles de collection de réseaux bipartites}
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\label{sec:extension-de-colsbm-aux-reseaux-bipartites}
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\section[Bipartite collection models]{Bipartite network collection models}
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\label{sec:extension-of-colsbm-to-bipartite-networks}
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\begin{frame}
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\frametitle{Collections bipartites}
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\frametitle{Bipartite collections}
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\[
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\forall m \in \{1\dots M\}, Y^m \overset{ind}{\sim} \mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1^m, Q_2^m, \pi^m, \rho^m, \alpha^m)
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\]
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\caption{Bristol}
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\end{subfigure}
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\begin{subfigure}[ht]{0.3\textwidth}
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\includestandalone[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh}
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\includegraphics[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Edinburgh.pdf}
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\caption{Edinburgh}
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\end{subfigure}
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\begin{subfigure}[ht]{0.3\textwidth}
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\includestandalone[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds}
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\includegraphics[width=1.1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2019_Leeds.pdf}
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\caption{Leeds}
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\end{subfigure}
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\caption{Matrices d'adjacence réordonnées, grâce au LBM}
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\caption{Reordered adjacency matrices, thanks to LBM}
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\label{fig:adj-reord}
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\end{figure}
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}
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\end{frame}
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\begin{frame}
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\frametitle{Différents modèles}
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\frametitle{Different models}
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\onslide<1->{ \begin{block}{\emph{iid}-colBiSBM}
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\[
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\forall m \in \{1\dots M\}, Y^m \overset{iid}{\sim}
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\mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1, Q_2, \pi, \rho, \alpha)
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\]
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avec $\theta = (\pi, \rho, \alpha)$.
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with $\theta = (\pi, \rho, \alpha)$.
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\end{block}}
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\onslide<2>{ \begin{block}{$\pi\rho$-colBiSBM}
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\[
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@ -173,53 +173,53 @@
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\mathcal{F}\text{-BiSBM}_{n_1^m,n_2^m}(Q_1, Q_2, \pi^m, \rho^m, \alpha)
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\]
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avec $\theta = ((\pi^m)_{m=1,\dots, M}, (\rho^m)_{m=1,\dots, M}, \alpha)$.
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with $\theta = ((\pi^m)_{m=1,\dots, M}, (\rho^m)_{m=1,\dots, M}, \alpha)$.
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\end{block}
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}
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\end{frame}
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\begin{frame}
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\frametitle{Estimation des paramètres}
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% DONE dire que tau i q m c' est la proba que Zim = q, approximation de la proba variationnelle. Parce qu on impose lindependance
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% Par maximisation d'une borne inférieure variationnelle de la
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% log-vraisemblance des données observées.
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Maximisation de la log-vraisemblance ?
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\begin{block}{log-vraisemblance et log-vraisemblance complète}
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\frametitle{Parameter estimation}
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% DONE say that tau i q m c' is the probability that Zim = q, approximation of the variational probability. Because we impose independence
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% By maximizing a variational lower bound of the
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% log-likelihood of the observed data.
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Maximizing the log-likelihood?
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\begin{block}{log-likelihood and complete log-likelihood}
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\[
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\ell(\bm{Y};\theta) = \sum_{\bm{Z,W}\in \bm{\mathcal{Z}\times\mathcal{W}}} \ell_c(\bm{Y}, \bm{Z}, \bm{W};\theta)
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\]
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avec $\bm{\mathcal{Z}} = \{1,\dots,\alert<2>{Q_1}\}^{\alert<2>{n}},
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with $\bm{\mathcal{Z}} = \{1,\dots,\alert<2>{Q_1}\}^{\alert<2>{n}},
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\bm{\mathcal{W}} = \{1,\dots,\alert<2>{Q_2}\}^{\alert<2>{n}}$
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\end{block}
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\uncover<3>{Donc, algorithme classique $\Rightarrow$
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\uncover<3>{So, classic algorithm $\Rightarrow$
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\emph{Expectation-Maximization} (EM).}
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\end{frame}
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\begin{frame}
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\frametitle{Par EM classique}
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A l'itération $(t)$ :
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\frametitle{By classic EM}
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At iteration $(t)$:
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\begin{itemize}
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\item[$\bullet$]\textbf{Étape E}: calculer
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\item[$\bullet$]\textbf{E Step}: calculate
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$$ \mathcal{Q}(\theta | \theta^{(t-1)}) = \mathbb E_{\alert<2>{\bm Z, \bm W | \bm Y, \theta^{(t-1)}} } \left[\ell_c(\bm Y, \bm W, \bm Z; \theta) \right] $$
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\item[$\bullet$]\textbf{Étape M}:
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\item[$\bullet$]\textbf{M Step}:
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$$ \theta^{(t)} = \arg \max_{\theta} \mathcal{Q}(\theta | \theta^{(t-1)})$$
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\end{itemize}
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\uncover<2>{
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\begin{alertblock}{Problème pour l'EM classique}
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Loi de $\bm{Z,W|Y},\theta^{(t-1)}$ inaccessible
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\begin{alertblock}{Problem for classic EM}
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Law of $\bm{Z,W|Y},\theta^{(t-1)}$ inaccessible
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\end{alertblock}}
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\end{frame}
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\begin{frame}
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Par \emph{Variational EM}, comme proposé
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par~\cite{daudinMixtureModelRandom2008,
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chabert-liddellLearningCommonStructures2024a}.
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\begin{block}{Approximation variationnelle de $\bm{Z,W|Y},\theta^{(t-1)}$}
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By \emph{Variational EM}, as proposed
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by~\cite{daudinMixtureModelRandom2008,
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chabert-liddellLearningCommonStructures2024}.
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\begin{block}{Variational approximation of $\bm{Z,W|Y},\theta^{(t-1)}$}
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$\mathcal{R}_{Y^m,\tau}(\mathbf{Z}^m, \mathbf{W}^m) =
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\mathcal{R}^1_{Y^m,\tau}(\mathbf{Z}^m)
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{\color{red}\times}
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\mathcal{R}^2_{Y^m,\tau}(\mathbf{W}^m) \Rightarrow$ indépendance lignes, colonnes.
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\mathcal{R}^2_{Y^m,\tau}(\mathbf{W}^m) \Rightarrow$ independence rows, columns.
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\end{block}
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\begin{multline*}
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\ell (\bm{Y};\theta) \geq \color{red}\sum_{m=1}^{M} \bigg(
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@ -229,13 +229,13 @@
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\color{red}\bigg) \color{black}
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\eqcolon \mathcal{J}(\tau;\theta)
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\end{multline*}
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où $\mathcal{Q}^m(\theta\mid\theta^{(t)}) =
|
||||
where $\mathcal{Q}^m(\theta\mid\theta^{(t)}) =
|
||||
\mathbb{E}_{\mathbf{Z}^m,\mathbf{W}^m
|
||||
\sim \mathcal{R}_{Y^m,\tau}(.)}
|
||||
\left[ \ell_c(Y^m,\mathbf{Z}^m,\mathbf{W}^m | \theta) \right] \,$
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Formule développée de l'EM variationnel}
|
||||
\begin{frame}{Developed formula of variational EM}
|
||||
\begin{multline*}
|
||||
\ell (\bm{Y};\theta) \geq \color{red}\sum_{m=1}^{M} \bigg( \color{black} \sum_{i = 1}^{n_1^m}\sum_{j=1}^{n_2^m}\sum_{q \in \mathcal{Q}_{1,m}} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{1,m}_{i,q} \tau^{2,m}_{j,r} \log f(Y^{m}_{ij}; \alpha_{qr}) \\
|
||||
+ \sum_{i=1}^{n_1^m} \sum_{q \in \mathcal{Q}_{1,m}} \tau^{1,m}_{i,q} \log \pi_{\color{black}q}^{\color{gray}m} + \sum_{j=1}^{n_2^m} \sum_{r \in \mathcal{Q}_{2,m}} \tau^{2,m}_{j,r} \log \rho_{\color{black}r}^{\color{gray}m} \\
|
||||
|
|
@ -243,13 +243,13 @@
|
|||
\mathcal{J}(\tau;\theta),
|
||||
\end{multline*}
|
||||
|
||||
\begin{block}{Approximation variationnelle}
|
||||
\begin{block}{Variational approximation}
|
||||
$\tau_{iq}^{1,m} = \mathcal{R}^1_{Y^m,\tau}(Z_{iq}^m = 1)$
|
||||
et $\tau_{jr}^{2,m} = \mathcal{R}^2_{Y^m,\tau}(W_{jr}^m = 1)$
|
||||
and $\tau_{jr}^{2,m} = \mathcal{R}^2_{Y^m,\tau}(W_{jr}^m = 1)$
|
||||
\end{block}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Étape \emph{Variational Expectation}}
|
||||
\begin{frame}{\emph{Variational Expectation} Step}
|
||||
\[
|
||||
\widehat{\tau}^{(t+1)} = \arg \max_{\tau}
|
||||
\mathcal{J}(\mathcal{\tau},\bm{\widehat{\theta}}^{(t)})
|
||||
|
|
@ -262,22 +262,22 @@
|
|||
\widehat{\tau}_{jr}^{2,m} \propto \widehat{\rho}_{r}^{m(t)} \prod_{i=1}^{n_1^m}\prod_{q\in\mathcal{Q}_1^m} f(Y_{ij}^m;\widehat{\alpha}_{qr}^{(t)})^{\widehat{\tau}_{iq}^{1,m(t+1)}} & \forall j = 1, \dots , n_2^m, r \in \mathcal{Q}_2^m
|
||||
\end{cases}
|
||||
\end{equation*}
|
||||
\footnotetext[2]{Initialisation des $\widehat{\tau}$ avec un
|
||||
\emph{spectral clustering} sur les réseaux.}
|
||||
\footnotetext[2]{Initialization of $\widehat{\tau}$ with a
|
||||
\emph{spectral clustering} on the networks.}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Étape \emph{Maximization}}
|
||||
\begin{frame}{\emph{Maximization} Step}
|
||||
\[
|
||||
\widehat{\theta}^{(t+1)} = \arg \max_{\theta} \mathcal{J}(\mathcal{\bm{\widehat{\tau}}}^{(t+1)},\theta)
|
||||
\]
|
||||
|
||||
\begin{block}{Paramètres de connectivité}
|
||||
\begin{block}{Connectivity parameters}
|
||||
\begin{align*}
|
||||
\widehat{\alpha}_{qr} = \frac{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \sum_{j=1}^{n_2^m} \tau_{iq}^{1,m} \tau_{jr}^{2,m} \alert<2>{Y_{ij}^m}}{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \sum_{j=1}^{n_2^m} \tau_{iq}^{1,m} \tau_{jr}^{2,m}}
|
||||
\end{align*}
|
||||
\end{block}
|
||||
\only<1>{
|
||||
\begin{block}{Proportions pour \emph{iid}}
|
||||
\begin{block}{Proportions for \emph{iid}}
|
||||
\begin{align*}
|
||||
\widehat{\pi}_q = \frac{\sum_{m=1}^{M} \sum_{i=1}^{n_1^m} \tau_{iq}^{1,m}}{\sum_{m=1}^{M} n_1^m} & &
|
||||
\widehat{\rho}_r = \frac{\sum_{m=1}^{M} \sum_{j=1}^{n_2^m} \tau_{jr}^{2,m}}{\sum_{m=1}^{M} n_2^m}
|
||||
|
|
@ -285,7 +285,7 @@
|
|||
\end{block}
|
||||
}
|
||||
\only<2>{
|
||||
\begin{block}{Proportions pour $\pi\rho$}
|
||||
\begin{block}{Proportions for $\pi\rho$}
|
||||
\begin{align*}
|
||||
\widehat{\pi}^{\color{red}m}_q = \frac{\sum_{i=1}^{n_1^m} \tau_{iq}^{1,m}}{n_1^m} & &
|
||||
\widehat{\rho}^{\color{red}m}_r = \frac{\sum_{j=1}^{n_2^m} \tau_{jr}^{2,m}}{n_2^m}
|
||||
|
|
@ -295,26 +295,26 @@
|
|||
|
||||
\end{frame}
|
||||
|
||||
\section{Sélection de modèle}
|
||||
\section{Model selection}
|
||||
\begin{frame}
|
||||
\frametitle{Problème choix de $(Q_1, Q_2)$}
|
||||
Besoin sélectionner $Q_1$ et $Q_2$. Critère BIC-Like\footnote{ICL + Entropie + pénalité}
|
||||
\frametitle{Problem of choosing $(Q_1, Q_2)$}
|
||||
Need to select $Q_1$ and $Q_2$. BIC-Like criterion\footnote{ICL + Entropy + penalty}
|
||||
|
||||
\begin{align*}
|
||||
\text{BIC-L}(\bm{Y}, Q_1, Q_2) & = \max_{\theta} \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\theta)] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2) \\
|
||||
& = \max_{\theta} \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \theta)} - \frac{1}{2}\text{pen}(\theta, Q_1, Q_2)
|
||||
\end{align*}
|
||||
|
||||
\begin{alertblock}{Problèmes de l'exploration}
|
||||
\begin{alertblock}{Exploration problems}
|
||||
\begin{itemize}
|
||||
\item Exploration de $\mathbb{N}^2$ coûteux.
|
||||
\item Sensibilité initialisations.
|
||||
\item Exploration of $\mathbb{N}^2$ costly.
|
||||
\item Sensitivity to initializations.
|
||||
\end{itemize}
|
||||
\end{alertblock}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Choix de $(Q_1,Q_2)$ - Approche gloutonne}
|
||||
\frametitle{Choice of $(Q_1,Q_2)$ - Greedy approach}
|
||||
\begin{columns}
|
||||
\begin{column}{0.5\linewidth}
|
||||
\begin{tikzpicture}
|
||||
|
|
@ -323,22 +323,22 @@
|
|||
\end{column}
|
||||
\begin{column}{0.35\linewidth}
|
||||
\begin{itemize}
|
||||
\item Modèle initialisé~:\\
|
||||
\item Initial model~:\\
|
||||
\begin{tikzpicture}
|
||||
\draw[fill=gray, draw=gray] circle [radius=0.225cm];
|
||||
\end{tikzpicture}
|
||||
\onslide<2->{
|
||||
\item Modèle après \emph{split}~:
|
||||
\item Model after \emph{split}~:
|
||||
\begin{tikzpicture}
|
||||
\draw[fill=blueind, draw=blueind] circle [radius=0.225cm];
|
||||
\end{tikzpicture}
|
||||
\item Modèle maximisant le critère~:\\
|
||||
\item Model maximizing the criterion~:\\
|
||||
\begin{tikzpicture}
|
||||
\draw[fill=white, draw=green, very thick] circle [radius=0.225cm];
|
||||
\end{tikzpicture}
|
||||
}
|
||||
\onslide<3->{
|
||||
\item Modèle après \emph{merge}~:
|
||||
\item Model after \emph{merge}~:
|
||||
\begin{tikzpicture}
|
||||
\draw[fill=red, draw=red] circle [radius=0.225cm];
|
||||
\end{tikzpicture}
|
||||
|
|
@ -348,23 +348,23 @@
|
|||
\end{columns}
|
||||
\end{frame}
|
||||
\begin{frame}
|
||||
\frametitle{Choix de $(Q_1,Q_2)$ - Fenêtre glissante}
|
||||
\frametitle{Choice of $(Q_1,Q_2)$ - Sliding window}
|
||||
\begin{columns}
|
||||
\begin{column}{0.6\textwidth}
|
||||
\begin{figure}
|
||||
\input{tikz/moving-window}
|
||||
\caption{Fenêtre glissante}
|
||||
\caption{Sliding window}
|
||||
\end{figure}
|
||||
\end{column}
|
||||
\begin{column}{0.4\textwidth}
|
||||
\only<3>{\begin{block}{}
|
||||
Initialisation du modèle si nécessaire
|
||||
Initialization of the model if necessary
|
||||
\end{block}}
|
||||
\only<9>{\begin{block}{}
|
||||
Localisation du nouveau mode
|
||||
Localization of the new mode
|
||||
\end{block}}
|
||||
\only<10>{\begin{block}{}
|
||||
Déplacement sur le nouveau mode puis itération
|
||||
Move to the new mode then iterate
|
||||
\end{block}}
|
||||
\end{column}
|
||||
\end{columns}
|
||||
|
|
@ -374,7 +374,7 @@
|
|||
\label{sec:application}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Résultats~\cite{baldockSystemsApproachReveals2019a}}
|
||||
\frametitle{Results~\cite{baldockSystemsApproachReveals2019}}
|
||||
|
||||
\only<1>{
|
||||
\begin{figure}[ht]
|
||||
|
|
@ -386,21 +386,21 @@
|
|||
\end{subfigure}\hfil
|
||||
\begin{subfigure}[t]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2019_Edinburgh}
|
||||
\includegraphics[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2019_Edinburgh.pdf}
|
||||
\caption{Edinburgh}
|
||||
\end{subfigure}
|
||||
\newline
|
||||
\begin{subfigure}[ht]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds}
|
||||
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Leeds.pdf}
|
||||
\caption{Leeds}
|
||||
\end{subfigure}\hfil
|
||||
\begin{subfigure}[ht]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Reading}
|
||||
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/mat-Baldock2019_Reading.pdf}
|
||||
\caption{Reading}
|
||||
\end{subfigure}
|
||||
\caption{Matrices d'adjacence,~\cite{baldockSystemsApproachReveals2019a}}
|
||||
\caption{Adjacency matrices,~\cite{baldockSystemsApproachReveals2019}}
|
||||
\end{figure}
|
||||
}
|
||||
\only<2>{
|
||||
|
|
@ -408,57 +408,57 @@
|
|||
\centering
|
||||
\begin{subfigure}[t]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol}
|
||||
\includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Bristol.pdf}
|
||||
\caption{Bristol}
|
||||
\end{subfigure}\hfil
|
||||
\begin{subfigure}[t]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh}
|
||||
\includegraphics[width=0.45\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Edinburgh.pdf}
|
||||
\caption{Edinburgh}
|
||||
\end{subfigure}
|
||||
\newline
|
||||
\begin{subfigure}[ht]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Leeds}
|
||||
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Leeds.pdf}
|
||||
\caption{Leeds}
|
||||
\end{subfigure}\hfil
|
||||
\begin{subfigure}[ht]{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Reading}
|
||||
\includegraphics[width=0.5\textwidth]{tikz/applications/baldock/colbisbm-mat-Baldock2019_Reading.pdf}
|
||||
\caption{Reading}
|
||||
\end{subfigure}
|
||||
\caption{Matrices d'adjacence réordonnée par \emph{iid}-colBiSBM,~\cite{baldockSystemsApproachReveals2019a}}
|
||||
\caption{Reordered adjacency matrices by \emph{iid}-colBiSBM,~\cite{baldockSystemsApproachReveals2019}}
|
||||
\end{figure}
|
||||
}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
\frametitle{Clustering de réseaux}
|
||||
\frametitle{Network clustering}
|
||||
\begin{figure}[ht]
|
||||
\includestandalone[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2011_TB+Baldock2011_JN}
|
||||
\caption{Matrice d'adjacence,~\cite{baldockDailyTemporalStructure2011}}
|
||||
\includegraphics[width=0.45\textwidth]{tikz/applications/baldock/mat-Baldock2011_TB+Baldock2011_JN.pdf}
|
||||
\caption{Adjacency matrix,~\cite{baldockDailyTemporalStructure2011}}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}[allowframebreaks]
|
||||
\frametitle{Application à~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019a}}
|
||||
\frametitle{Application to~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019}}
|
||||
\begin{figure}[t]
|
||||
\centering
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=0.2,angle=-90]{backup-app-iid.png}
|
||||
\caption{Modèle $iid$}
|
||||
\caption{Model $iid$}
|
||||
\end{subfigure}%
|
||||
~
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=0.2,angle=-90]{backup-app-pirho.png}
|
||||
\caption{Modèle $\pi\rho$}
|
||||
\caption{Model $\pi\rho$}
|
||||
\end{subfigure}%
|
||||
\caption{Partitionnement des réseaux
|
||||
de~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019a}}
|
||||
\caption{Partitioning of networks
|
||||
of~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019}}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[t]
|
||||
|
|
@ -467,23 +467,23 @@
|
|||
\centering
|
||||
\includegraphics[scale=0.1]{backup-app-iid-struct1.png}
|
||||
\includegraphics[scale=0.2]{backup-app-iid-struct2.png}
|
||||
\caption{Modèle $iid$,\\
|
||||
séparent réseau africain et réseaux anglais}
|
||||
\caption{Model $iid$,\\
|
||||
separate African network and English networks}
|
||||
\end{subfigure}%
|
||||
~
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=0.2]{backup-app-pirho-struct.png}
|
||||
\caption{Modèle $\pi\rho$,\\
|
||||
fusionnent réseaux africain et anglais}
|
||||
\caption{Model $\pi\rho$,\\
|
||||
merge African and English networks}
|
||||
\end{subfigure}%
|
||||
\caption{Structures détectées pour les réseaux
|
||||
de~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019a}}
|
||||
\caption{Structures detected for networks
|
||||
of~\cite{baldockDailyTemporalStructure2011,
|
||||
baldockSystemsApproachReveals2019}}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Algorithme du clustering}
|
||||
\begin{frame}{Clustering algorithm}
|
||||
\centering
|
||||
\vspace{0.25\baselineskip}
|
||||
\begin{tikzpicture}[scale=0.85]
|
||||
|
|
@ -494,38 +494,38 @@
|
|||
\]
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Résultats}
|
||||
\begin{frame}{Results}
|
||||
\begin{figure}[ht]
|
||||
\centering
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2011_TB+Baldock2011_JN}
|
||||
\caption{Réordonnée par LBM}
|
||||
\includegraphics[width=1\textwidth]{tikz/applications/baldock/bisbm-mat-Baldock2011_TB+Baldock2011_JN.pdf}
|
||||
\caption{Reordered by LBM}
|
||||
\end{subfigure}\hfil
|
||||
\begin{subfigure}{0.5\textwidth}
|
||||
\centering
|
||||
\includestandalone[width=1\textwidth]{tikz/applications/baldock/pirho-colbisbm-mat-Baldock2011_TB+Baldock2011_JN}
|
||||
\caption{Réordonnée par $\pi\rho$-colBiSBM}
|
||||
\includegraphics[width=1\textwidth]{tikz/applications/baldock/pirho-colbisbm-mat-Baldock2011_TB+Baldock2011_JN.pdf}
|
||||
\caption{Reordered by $\pi\rho$-colBiSBM}
|
||||
\end{subfigure}
|
||||
|
||||
\caption{Matrice d'adjacence réordonnée par $\pi\rho$-colBiSBM,~\cite{baldockDailyTemporalStructure2011}}
|
||||
\caption{Reordered adjacency matrix by $\pi\rho$-colBiSBM,~\cite{baldockDailyTemporalStructure2011}}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
|
||||
\section{Conclusion}
|
||||
\label{sec:conclusion}
|
||||
\begin{frame}
|
||||
\frametitle{Conclusion et perspectives}
|
||||
% DONE Ajouter une slide conclusion perspective
|
||||
% Rappeler les modeles avec clustering
|
||||
% Evoquer l'analyse de reseaux corrigés pour l'échantillonnage
|
||||
% Lien vers le package
|
||||
\begin{block}{Capacités}
|
||||
\frametitle{Conclusion and perspectives}
|
||||
% DONE Add a conclusion perspective slide
|
||||
% Recall models with clustering
|
||||
% Mention analysis of corrected networks for sampling
|
||||
% Link to the package
|
||||
\begin{block}{Capabilities}
|
||||
\begin{itemize}
|
||||
\item 4 modèles dont 3 qui ont une flexibilité sur au moins une des
|
||||
dimensions (adaptabilité aux données).
|
||||
\item Détecter structures classiques et moins classique de façon agnostique.
|
||||
\item Partitionner un ensemble de réseaux selon leurs structures.
|
||||
\item 4 models including 3 with flexibility on at least one of
|
||||
the dimensions (adaptability to data).
|
||||
\item Detect classic and less classic structures in an agnostic way.
|
||||
\item Partition a set of networks according to their structures.
|
||||
\end{itemize}
|
||||
\end{block}
|
||||
|
||||
|
|
@ -533,22 +533,22 @@
|
|||
|
||||
\begin{frame}{Perspectives}
|
||||
\begin{itemize}
|
||||
\item Investiguer stabilité face à l'aléatoire et aux \emph{optima} locaux.
|
||||
\item Preuve d'identifiabilité du modèle $\pi\rho$.
|
||||
\item Investigate stability against randomness and local \emph{optima}.
|
||||
\item Proof of identifiability of the $\pi\rho$ model.
|
||||
\end{itemize}
|
||||
|
||||
\begin{block}{Package et applications}
|
||||
\begin{block}{Package and applications}
|
||||
\begin{itemize}
|
||||
\item Intégration au package \texttt{colSBM}, amélioration interface utilisateur et
|
||||
ajout retours écologues
|
||||
\item Publication CRAN
|
||||
\item Intégrer possibilité d'un critère supplémentaire pour le clustering
|
||||
\item Appliquer clustering données de
|
||||
\item Integration into the \texttt{colSBM} package, improvement of user interface and
|
||||
addition of ecologists' feedback
|
||||
\item CRAN publication
|
||||
\item Integrate the possibility of an additional criterion for clustering
|
||||
\item Apply clustering to data from
|
||||
\cite{pichonTellingMutualisticAntagonistic2024,doreRelativeEffectsAnthropogenic2021}
|
||||
\end{itemize}
|
||||
|
||||
\end{block}
|
||||
\bigskip
|
||||
\centering
|
||||
Merci pour votre attention~!
|
||||
Thank you for your attention~!
|
||||
\end{frame}
|
||||
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