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node}=[fill=green!50!blue!20!white] + \node[state] (N1) at (1.1,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; + \node[state, right = of N1] (N2) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (.75,3) + \node[state, right = of N2] (N3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (1.5,3) + \node[state, right = of N3] (N4) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (2.25,3) + % \node[state] (N5) at (3,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; + % \node[state] (N6) at (3.75,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; + + \tikzstyle{every node}=[shape=rectangle,fill=red!50!blue!20!white] + % \node[state, fill = white] (P) at (-1.5, 0) {\includegraphics[width=.08\textwidth]{img/bee.png}}; + \node[state, tokens=0] (P1) at (-1, 0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; + \node[state, tokens=0, right = of P1] (P2) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (-.25, 0) + \node[state, tokens=0, right = of P2] (P3) {\includegraphics[width=.1\textwidth]{img/bee.png}}; %at (.5, 0) + \node[state, tokens=0, right = of P3] (P4) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (1.25, 0) + \node[state, tokens=0, right = of P4] (P5) {\includegraphics[width=.1\textwidth]{img/bee.png}};% at (2,0) + \node[state, tokens=0, right = of P5] (P6) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (2.75,0) + % \node[state, tokens=0] (P7) at (3.5,0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; + % \node[state, tokens=0] (P8) at (4.25,0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; + + \tikzstyle{every edge}=[>=stealth,shorten >=1pt,auto,thin,draw] + \path (P1) edge (N1); + \path (P2) edge (N1); + \path (P3) edge (N1); + \path (P4) edge (N2); + \path (P4) edge (N1); + \path (P6) edge (N2); + \path (P1) edge (N3); + %\path (P7) edge (N4); + %\path (P8) edge (N5); + %\path (P4) edge (N6); + \path (P5) edge (N3); + \path (P5) edge (N4); + \end{tikzpicture} + \caption{Exemple d'un réseau plantes-pollinisateurs} + \label{fig:plantes-pollin} + \end{figure} + + \item En écologie microbienne réseaux permettent le suivi de la + qualité des sols. + % En écologie microbienne, les réseaux sont construits sur la base + % de co-occurences et reconstruits par inférence des liens mais + % rarement par observation directe. \end{itemize} - \begin{figure}[ht] - \centering - \begin{tikzpicture}[scale=.6] - \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,thin,draw] - \tikzstyle{every state}=[draw, text=white,scale=0.65, font=\scriptsize, transform shape] - - % Upper level - \tikzstyle{every state}=[draw=none,text=white,scale=0.55, font=\scriptsize, transform shape] - % premier cluster - \tikzstyle{every node}=[fill=green!50!blue!20!white] - \node[state] (N1) at (1.1,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; - \node[state, right = of N1] (N2) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (.75,3) - \node[state, right = of N2] (N3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (1.5,3) - \node[state, right = of N3] (N4) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (2.25,3) - % \node[state] (N5) at (3,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; - % \node[state] (N6) at (3.75,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; - - \tikzstyle{every node}=[shape=rectangle,fill=red!50!blue!20!white] - % \node[state, fill = white] (P) at (-1.5, 0) {\includegraphics[width=.08\textwidth]{img/bee.png}}; - \node[state, tokens=0] (P1) at (-1, 0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; - \node[state, tokens=0, right = of P1] (P2) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (-.25, 0) - \node[state, tokens=0, right = of P2] (P3) {\includegraphics[width=.1\textwidth]{img/bee.png}}; %at (.5, 0) - \node[state, tokens=0, right = of P3] (P4) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (1.25, 0) - \node[state, tokens=0, right = of P4] (P5) {\includegraphics[width=.1\textwidth]{img/bee.png}};% at (2,0) - \node[state, tokens=0, right = of P5] (P6) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (2.75,0) - % \node[state, tokens=0] (P7) at (3.5,0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; - % \node[state, tokens=0] (P8) at (4.25,0) {\includegraphics[width=.1\textwidth]{img/bee.png}}; - - \tikzstyle{every edge}=[>=stealth,shorten >=1pt,auto,thin,draw] - \path (P1) edge (N1); - \path (P2) edge (N1); - \path (P3) edge (N1); - \path (P4) edge (N2); - \path (P4) edge (N1); - \path (P6) edge (N2); - \path (P1) edge (N3); - %\path (P7) edge (N4); - %\path (P8) edge (N5); - %\path (P4) edge (N6); - \path (P5) edge (N3); - \path (P5) edge (N4); - \end{tikzpicture} - \caption{Exemple d'un réseau plantes-pollinisateurs} - \label{fig:plantes-pollin} - \end{figure} \end{frame} \begin{frame}{Contexte mathématique} - \begin{itemize} - \item Faire de la détection de structure réseau par réseau de manière - agnostique (SBM, LBM) est bien connu. Mais il y a de l'intérêt à - le faire sur plusieurs : - \begin{itemize} - \item Des espèces différentes dans plusieurs réseaux pourrait - remplir des rôles similaires - \item Les petits réseaux pourraient bénéficier d'une estimation - avec des réseaux plus grands et révéler une structure plus - fine. - \item Certains réseaux étant moins bien échantillonnés que - d'autre une prise en compte en collection de réseaux pourrait - aider à transférer de l'information - \end{itemize} - \item Re-grouper les réseaux selon leur similarité (\emph{clustering} + + Détection de structure\footnote{L'organisation du réseau.} pour un réseau + bien connu : + \begin{itemize} + \item Modèles de \emph{clustering} à variables latentes + \item \emph{Embedding} par apprentissage profond + \end{itemize} + + Mais des motivations pour considérer des collections : + \begin{itemize} + \item Espèces différentes, rôles analogues + % Des espèces différentes dans plusieurs réseaux pourrait + % remplir des rôles similaires + \item Transfert d'informations grands vers petits réseaux. + % Les petits réseaux pourraient bénéficier d'une estimation + % avec des réseaux plus grands et révéler une structure plus + % fine. + % Certains réseaux étant moins bien échantillonnés que + % d'autre une prise en compte en collection de réseaux pourrait + % aider à transférer de l'information + \item Regrouper les réseaux selon leur similarité (\emph{clustering} de réseaux) - \item Transférer de l'information grâce à la collection (par exemple - reconstitution de données manquantes) - \item Proposer des comparaisons en extrayant plus d'informations que - les métriques classiques \end{itemize} \end{frame} @@ -176,10 +185,137 @@ \end{column} \end{columns} \smallskip - Permet de décrire des interactions impliquant deux agents dont les rôles - sont de natures différentes.\\ - Par exemple : hôtes-parasites, plantes-pollinisateurs, graines-disperseurs - \dots + Décrit des interactions (pas uniquement binaires) entre deux groupes d'agents : + \begin{itemize} + \item hôtes-parasites + \item plantes-pollinisateurs + \item graines-disperseurs\newline + \vdots + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Latent Block Model (LBM)} + Proposé par~\cite{govaertEMAlgorithmBlock2005}. + \begin{columns} + \begin{column}{0.40\linewidth} + \begin{figure}[H] + \center + \begin{tikzpicture}[scale=0.35] + \tikzstyle{every state}=[draw, text=black,scale=0.95, + transform shape] + \tikzstyle{every state}=[draw=none,text=black,scale=0.75, + transform shape] + \tikzset{edge_proba/.style={draw=white, fill=none, + text=black}} + + \tikzstyle{every node}=[fill=blueind] + \node[edge_proba] (pi1) at (1,5.7) + {\textbf{$\pi_{{\color{blueind}\bullet}}$}}; + \node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}}; + \node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}}; + \node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}}; + + \tikzstyle{every node}=[fill=cyanind] + \node[edge_proba] (pi2) at (6.75,5.7) + {\textbf{$\pi_{{\color{cyanind}\bullet}}$}}; + \node[state, draw=black!50] (R21) at (6.25,5) + {\textbf{R21}}; + \node[state, draw=black!50] (R22) at (7.25,5) + {\textbf{R22}}; + + \tikzstyle{every node}=[fill=electricblue] + \node[edge_proba] (pi3) at (10,5.7) + {\textbf{$\pi_{{\color{electricblue}\bullet}}$}}; + \node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}}; + + \tikzstyle{every node}=[fill=burntorange, shape=rectangle] + \node[edge_proba] (pi3) at (0.5,-0.7) + {\textbf{$\rho_{{\color{burntorange}\bullet}}$}}; + \tikzstyle{every state}=[draw=none,text=black,scale=0.75, + transform shape, shape=rectangle] + \node[state, draw=black!50] (B1) at (0,0) {\textbf{C11}}; + \node[state, draw=black!50] (B2) at (1,0) {\textbf{C12}}; + \tikzstyle{every node}=[fill=goldenyellow, shape=rectangle] + \node[edge_proba] (pi3) at (4,-0.7) + {\textbf{$\rho_{{\color{goldenyellow}\bullet}}$}}; + \node[state, draw=black!50] (B3) at (3.5,0) {\textbf{C21}}; + \node[state, draw=black!50] (B4) at (4.5,0) {\textbf{C22}}; + \tikzstyle{every node}=[fill=peach, shape=rectangle] + \node[edge_proba] (pi3) at (10,-0.7) + {\textbf{$\rho_{{\color{peach}\bullet}}$}}; + \node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}}; + + \tikzstyle{every edge}=[-,>=stealth',shorten + >=1pt,auto,draw,line width=1.5pt,draw opacity=0.2] + + \path (R11) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[left, + fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$} + (B1); + \path (R11) edge (B2); + \path (R11) edge (B3); + \path (R11) edge (B4); + + \path (R12) edge [] (B1); + \path (R12) edge (B2); + \path (R12) edge (B3); + \path (R12) edge (B4); + + \path (R13) edge [] (B1); + \path (R13) edge (B2); + \path (R13) edge (B3); + \path (R13) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{goldenyellow}\bullet}}$} + (B4); + + \path (R21) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right, fill=none] + {$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3); + \path (R21) edge (B4); + \path (R21) edge (B5); + + \path (R22) edge (B3); + \path (R22) edge (B4); + \path (R22) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, left, + fill=none] {$\alpha_{{\color{cyanind}\bullet}{\color{peach}\bullet}}$} (B5); + + \path (R31) edge[-,>=stealth',shorten + >=1pt,auto,draw=gray,line width=1.5pt, fill=gray, opacity=1] node[midway, + right, fill=none] + {$\alpha_{{\color{electricblue}\bullet}{\color{peach}\bullet}}$} (B5); + + \end{tikzpicture} + \caption{Exemple de LBM\footnotemark} + \label{fig:LBMvisu-principal} + \end{figure} + \end{column} + \footnotetext[2]{Que j'appelle par la suite BiSBM} + \begin{column}{0.51\linewidth} + \newline + Pour \begin{itemize} + \item $Q_1 = + |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ + blocs fixés en ligne + \item $Q_2 = + |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ + blocs fixés en colonne + \end{itemize} + \begin{block}{Paramètres} + \begin{itemize} + \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ en ligne + et $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + \item + $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = + \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = + {\color{burntorange}\bullet})$ + \end{itemize} + \end{block} + \end{column} + \end{columns} \end{frame} \begin{frame} @@ -277,8 +413,10 @@ \end{scope} \begin{scope}[xshift=3cm, yshift = 1cm] - \node[text justified, fill=none] at (10, 3.5) - {$\overset{iid}{\sim}$}; + \only<1>{\node[text justified, fill=none] at (10, 3.5) + {$\overset{iid}{\sim}$};} + \only<2>{\node[text justified, fill=none] at (10, 3.5) + {$\sim$};} \begin{scope}[yshift = 6cm] \tikzstyle{every state}=[draw, text=black,scale=0.75, transform shape] @@ -297,6 +435,12 @@ \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^1 = $}; + + \node[state, draw=black!50] (B1) at (0.5,-1) {\textbf{1}}; @@ -349,6 +493,10 @@ \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle] + % Label réseau + \node[font=\small, text justified,draw=none, fill=none, + below left = 0.04cm of R11] {$Y^M = $}; + \node[state, draw=black!50] (B1) at (0.5,0) {\textbf{5}}; \node[state, draw=black!50] (B2) at (1.5,0) @@ -383,35 +531,138 @@ \end{adjustbox} \end{center} - Pour + \only<1>{ + \begin{block}{Modèle $iid$-colBiSBM} + $$\forall m \in [\![ 1, M ]\!], Y_i \sim LBM_{n^m_1, n^m_2} (\pi, \rho, \alpha)$$ + \end{block} + } + \only<2>{ + \begin{block}{Modèle $\pi\rho$-colBiSBM} + $$\forall m \in [\![ 1, M ]\!], Y_i \sim LBM_{n^m_1, n^m_2} (\pi^{\color{red}m}, \rho^{\color{red}m}, \alpha)$$ + \end{block} + } + % Pour + % \begin{itemize} + % \item $Q_1 = + % |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ + % blocs fixés en ligne + % \item $Q_2 = + % |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ + % blocs fixés en colonne + % \end{itemize} + % \begin{block}{Paramètres} + % \begin{itemize} + % \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et + % $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne + % \item + % $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = + % \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = + % {\color{burntorange}\bullet})$ + % \end{itemize} + % \end{block} +\end{frame} +\begin{frame}{Apport déjà réalisé} \begin{itemize} - \item $Q_1 = - |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ - blocs fixés en ligne - \item $Q_2 = - |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ - blocs fixés en colonne + \item Écriture du modèle colBiSBM + \item Dérivation des formules d'inférence et d'un critère de sélection + de modèle de vraisemblance pénalisée + \item Implémentation des formules et du critère et développement + algorithmique pour l'exploration de l'espace de paramètres. + \note[item]{Principalement pendant mon premier stage} + \item Partitionnement d'une large collection de réseaux. + \item Écriture du code s'intégrant au package\footnote{ + \scalebox{0.8}{\faGithub + \url{https://github.com/Chabert-Liddell/colSBM}}} + écrit par Saint-Clair Chabert-Liddell. + \note[item]{Pendant mon stage actuel} \end{itemize} - \begin{block}{Paramètres} - \begin{itemize} - \item $\pi_{\bullet} = \mathbb{P}(Z_i =\bullet)$ en ligne et - $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ en colonne - \item - $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = - \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = - {\color{burntorange}\bullet})$ - \end{itemize} - \end{block} + \end{frame} \begin{frame} - \frametitle{Application, données plantes pollinisateurs} + \frametitle{Clustering de réseaux} + \begin{columns} + \begin{column}{0.2\linewidth} + \begin{block}{Objectif} + Déterminer une partition qui maximise la somme du critère de ses + sous-collections. + \end{block} + \end{column} + \begin{column}{0.78\linewidth} + \begin{tikzpicture}[scale=0.6, every node/.style={scale=0.75}] + \tikzstyle{instruct}=[font=\small, text justified, + rectangle,draw,fill=yellow!50] + \tikzstyle{first_col}=[rectangle, text justified, + draw,fill=gray!50] + \tikzstyle{second_col}=[scale=0.55, circle, draw,fill=red!50] + \tikzstyle{test}=[font=\small, text justified, diamond, + aspect=2.5,thick, + draw=blue,fill=yellow!50,text=blue] + \tikzstyle{es}=[font=\small, text justified, + rectangle,draw,rounded corners=4pt,fill=cyanind!25] + + \node[es] (liste) at (0,4) {Donner une collection à + partitionner}; + \node[instruct, text width=5cm, below = 0.45cm of liste] + (1-collection) {Ajuster \emph{colBiSBM}}; + \node[first_col, right = 0.5cm of 1-collection] (1-col-obj) {}; + \node[instruct, text width=5cm, below = 0.45cm of 1-collection] + (dissimi) {Calculer une matrice de dissimilarité de la collection}; + \node[instruct, text width=5cm, below = 0.45cm of dissimi] + (2-sous-collection) {Séparer la \emph{collection en 2 sous-collections} et + ajuster les \emph{colBiSBM}}; + \node[second_col, right = 0.25cm of 2-sous-collection] + (1-sec-col-obj) {1}; + \node[second_col, right = 0.25cm of 1-sec-col-obj] + (1-sec-col-obj) {2}; + \node[test,below = 0.45cm of 2-sous-collection, scale=0.5] + (BICL-test) {$\sum_{i=1}^{2} + (\text{BIC-L}(\tikz[baseline=-0.25cm]{\node[second_col] {i};} )) > + \text{BIC-L}(\tikz[baseline=-0.25cm]{\node[first_col] {};})$?}; + \node[es, right = 0.55cm of BICL-test] (sortie) {Renvoyer + \tikz{\node[rectangle, draw, fill=gray!50, rounded corners=0pt] {};}}; + \node[es, left = 0.45cm of dissimi, text width = 2cm] + (recursion) {Recommencer sur \tikz{\node[second_col] {1};} et + \tikz{\node[second_col] {2};} }; + + \tikzstyle{suite}=[->,>=stealth,thick,rounded corners=4pt] + \draw[suite] (liste) -- (1-collection); + \draw[suite] (1-collection) -- (dissimi); + \draw[suite] (dissimi) -- (2-sous-collection); + \draw[suite] (2-sous-collection) -- (BICL-test); + \draw[suite] (BICL-test) -| node[near start, above, fill=none] + {Oui} (recursion); + \draw[suite] (recursion.north) |- (1-collection.west); + \draw[suite] (BICL-test) -- node[near start, above, fill=none] + {Non} (sortie); + + \end{tikzpicture} + \end{column} + \end{columns} + \blfootnote{Même approche + que~\cite{chabert-liddellLearningCommonStructures2024}} +\end{frame} + + + +\begin{frame} + \frametitle{Application du \emph{clustering}, données plantes pollinisateurs} \small Voici des résultats du modèle \emph{iid-colBiSBM} sur des données plantes-pollinisateurs (\cite{doreRelativeEffectsAnthropogenic2021} et~\cite{thebaultDatabasePlantpollinatorNetworks2020}) % DONE Ajouter un tableau avec le nombre de réseaux dans chaque sous-collection \begin{columns} + \begin{column}{0.49\linewidth} + \begin{figure}[H] + \includegraphics[width=0.35\textwidth]{img/iid-meso-1.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-2.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-3.png} + \includegraphics[width=0.35\textwidth]{img/iid-meso-4.png} + \includegraphics[width=0.30\textwidth]{img/iid-meso-5.png} + \caption{Connectivités de la partition} + \end{figure} + \end{column} \begin{column}{0.49\linewidth} \includegraphics[scale=0.30]{img/annual_time_span_vs_iid.png} @@ -429,48 +680,25 @@ \end{center} \end{column} - \begin{column}{0.49\linewidth} - \begin{figure}[H] - \includegraphics[width=0.30\textwidth]{img/iid-meso-1.png} - \includegraphics[width=0.30\textwidth]{img/iid-meso-2.png} - \includegraphics[width=0.30\textwidth]{img/iid-meso-3.png} - \includegraphics[width=0.30\textwidth]{img/iid-meso-4.png} - \includegraphics[width=0.30\textwidth]{img/iid-meso-5.png} - \caption{Connectivités de la partition} - \end{figure} - \end{column} \end{columns} \end{frame} -\begin{frame} - \begin{block}{Apport déjà réalisé} - \small +\begin{frame}{À faire} \begin{itemize} - \item Adaptation du modèle mathématique\footnote{\scalebox{0.8}{Notamment des formules des étapes VE - et M et du calcul de dissimilarité.}} proposé par - \cite{chabert-liddellLearningCommonStructures2024} aux réseaux bipartites - \item Développement algorithmique pour l'exploration de l'espace de - paramètres. - \item Écriture du code de la partie bipartite s'intégrant - au package\footnote{\scalebox{0.8}{\faGithub - \url{https://github.com/Chabert-Liddell/colSBM}}} écrit par Saint-Clair Chabert-Liddell. - \end{itemize} - \end{block} - - \begin{block}{À finir/à faire} - \small - \begin{itemize} - \item Finaliser l'analyse d'applications sur données réelles + \item Finaliser l'analyse sur données réelles commencée sur \cite{doreRelativeEffectsAnthropogenic2021, thebaultDatabasePlantpollinatorNetworks2020} avec les - interprétations des écologues. + interprétations des écologues en vue d'une publication. + \note[item]{Dans \emph{Methods in Ecology and Evolution}} \item Preuve d'identifiabilité du modèle \parencite{chabert-liddellLearningCommonStructures2024, celisseConsistencyMaximumlikelihoodVariational2012, keribinEstimationSelectionLatent2015, braultCoclusteringLatentBloc2015} + \note[item]{Car les blocs vides du modèles $\pi\rho$ posent + soucis.} + \end{itemize} - \end{block} \end{frame} @@ -485,34 +713,37 @@ \end{figure} - En utilisant les \emph{Graph Convolutional Networks} (GCN) - il est possible de réaliser un \emph{embedding} des graphes - \parencite{velickovicGraphAttentionNetworks2018,hamiltonInductiveRepresentationLearning, xuHowPowerfulAre2019} en - tenant compte des invariances qui sont inhérentes à ces objets. + Avec les \emph{Graph Convolutional Networks} (GCN) \emph{embedding} de graphes + \parencite{velickovicGraphAttentionNetworks2018,hamiltonInductiveRepresentationLearning, + xuHowPowerfulAre2019} tenant compte des invariances. \begin{block}{Règle de propagation d'une couche de GCN} - \begin{equation} - H^{(l+1)} = \sigma \bigl( \tilde{D}^{\frac{1}{2}} \tilde{A} \tilde{D}^{\frac{1}{2}} H^{(l)} W^{(l)} \bigr), - \end{equation} - tirée de \cite{kipfSemiSupervisedClassificationGraph2017}. + \begin{equation} + H^{(l+1)} = \sigma \bigl( \tilde{D}^{\frac{1}{2}} \tilde{A} \tilde{D}^{\frac{1}{2}} H^{(l)} W^{(l)} \bigr), + \end{equation} + tirée de \cite{kipfSemiSupervisedClassificationGraph2017}. \end{block} + \begin{itemize} + \item Utiliser des \emph{Variational Auto-Encoder} (VAE) + \parencite{ + kipfVariationalGraphAutoEncoders2016, + kipfSemiSupervisedClassificationGraph2017} et + résume le réseau par une distribution. Calculer distance de + Gromov-Wasserstein pour comparaison et classification.\\ - Pour, par exemple, utiliser des auto-encodeur variationnels ou VAE - \parencite{ - kipfVariationalGraphAutoEncoders2016, - kipfSemiSupervisedClassificationGraph2017} par exemple et - donc permettant d'obtenir par réseau une distribution. Cela permet alors - par exemple de calculer une distance de Gromov-Wasserstein afin de comparer - les réseaux et de pouvoir réaliser un \emph{clustering} ou une - classification.\\ + Un des avantages principaux est le \emph{passage à l'échelle} de ces méthodes + permettant de traiter des réseaux de plus grande taille. + \end{itemize} - Un des avantages principaux est le \emph{passage à l'échelle} de ces méthodes - permettant de traiter des réseaux de plus grande taille. \end{frame} \subsection[Axe 3]{Axe 3 : Inférence jointe de réseaux} \label{sec:axe-3} \begin{frame} + En écologie, réseaux inférés à partir de table de co-occurences. + TODO Insérer une table de co-occurence + Incertitude connue mais négliger dans la suite de l'analyse. + Limites des techniques actuelles \cite{matchadoNetworkAnalysisMethods2021}. Rôle important pour les réseaux reconstruits notamment en microbiologie. \end{frame} @@ -524,11 +755,11 @@ \begin{figure}[ht] \centering \begin{chronology}[1]{2024}{2028}{\textwidth}[110ex] - \eventspan {\decimaldate{1}{10}{2024}}{\decimaldate{1}{10}{2025}}% + \eventspan {\decimaldate{1}{10}{2024}}{\decimaldate{1}{6}{2025}}% {\small\textbf{\color{blue} Collections \& modèles à variables latentes}}[blue][.3][0.1] \eventspan {\decimaldate{1}{5}{2025}}{\decimaldate{1}{10}{2026}}% {\textbf{\color{red} \emph{Embedding} de n\oe uds par \emph{Deep Learning}}}[red][.3][0.1] - \eventspan {\decimaldate{1}{4}{2026}}{\decimaldate{1}{4}{2027}}% + \eventspan {\decimaldate{1}{3}{2026}}{\decimaldate{1}{4}{2027}}% {\textbf{\color{ao(english)} Inférence jointe de réseaux}}[ao(english)][.3][0.1] \eventspan {\decimaldate{1}{4}{2027}}{\decimaldate{1}{10}{2027}}% {\textbf{\color{gray} Rédaction du manuscrit}}[gray][.3][0.1][b] @@ -538,7 +769,7 @@ % \eventpoint{\decimaldate{26}{10}{2004}}{Ubuntu 4.10}[red][1][1] % \eventspan {\decimaldate{25}{8}{1991}}{\decimaldate{31}{8}{2023}}% % {\textbf{\color{orange}Linux}}[orange][.6][.6][b] - \end{chronology} + \end{chronology} \caption{Chronologie prévue} \label{fig:chronologie} \end{figure} @@ -562,9 +793,3 @@ \huge Merci pour votre attention. \vfill \end{frame} - -\renewcommand{\pgfuseimage}[1]{\scalebox{.75}{\includegraphics{#1}}} -\begin{frame}[noframenumbering,plain,allowframebreaks] - \frametitle{Bibliographie} - \printbibliography -\end{frame} diff --git a/references.bib b/references.bib index f8ea74d..0979191 100644 --- a/references.bib +++ b/references.bib @@ -269,6 +269,24 @@ file = {/home/polarolouis/Zotero/storage/YIUG7VAU/Hamilton et al. - Inductive Representation Learning on Large Graphs.pdf} } +@article{hoffLatentSpaceApproaches2002, + title = {Latent {{Space Approaches}} to {{Social Network Analysis}}}, + author = {Hoff, Peter D and Raftery, Adrian E and Handcock, Mark S}, + date = {2002-12-01}, + journaltitle = {Journal of the American Statistical Association}, + volume = {97}, + number = {460}, + pages = {1090--1098}, + publisher = {Taylor \& Francis}, + issn = {0162-1459}, + doi = {10.1198/016214502388618906}, + url = {https://doi.org/10.1198/016214502388618906}, + urldate = {2024-05-20}, + abstract = {Network models are widely used to represent relational information among interacting units. In studies of social networks, recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors. We develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved “social space.” We make inference for the social space within maximum likelihood and Bayesian frameworks, and propose Markov chain Monte Carlo procedures for making inference on latent positions and the effects of observed covariates. We present analyses of three standard datasets from the social networks literature, and compare the method to an alternative stochastic blockmodeling approach. In addition to improving on model fit for these datasets, our method provides a visual and interpretable model-based spatial representation of social relationships and improves on existing methods by allowing the statistical uncertainty in the social space to be quantified and graphically represented.}, + keywords = {Conditional independence model,Latent position model,Network data,Random graph,Visualization}, + file = {/home/polarolouis/Zotero/storage/7UYRBBA2/Hoff et al. - 2002 - Latent Space Approaches to Social Network Analysis.pdf;/home/polarolouis/Zotero/storage/R4TGSVGP/016214502388618906.pdf.pdf} +} + @article{hollandStochasticBlockmodelsFirst1983, title = {Stochastic Blockmodels: {{First}} Steps}, shorttitle = {Stochastic Blockmodels}, @@ -498,6 +516,23 @@ file = {/home/polarolouis/Zotero/storage/4A3V4EFV/gnn-intro.html} } +@article{sewellLatentSpaceModels2015, + title = {Latent {{Space Models}} for {{Dynamic Networks}}}, + author = {Sewell, Daniel K. and Chen, Yuguo}, + date = {2015-10-02}, + journaltitle = {Journal of the American Statistical Association}, + volume = {110}, + number = {512}, + pages = {1646--1657}, + publisher = {Taylor \& Francis}, + issn = {0162-1459}, + doi = {10.1080/01621459.2014.988214}, + url = {https://www.tandfonline.com/doi/full/10.1080/01621459.2014.988214}, + urldate = {2024-05-20}, + keywords = {Embedding,Markov chain Monte Carlo,Network data,Social influence,Visualization}, + file = {/home/polarolouis/Zotero/storage/6LJMITGR/Sewell et Chen - 2015 - Latent Space Models for Dynamic Networks.pdf;/home/polarolouis/Zotero/storage/TJD8ZWBA/01621459.2014.988214.pdf.pdf} +} + @article{snijdersEstimationPredictionStochastic1997, title = {Estimation and {{Prediction}} for {{Stochastic Blockmodels}} for {{Graphs}} with {{Latent Block Structure}}}, author = {Snijders, Tom A.B. and Nowicki, Krzysztof}, @@ -617,6 +652,26 @@ file = {/home/polarolouis/Zotero/storage/THBD5QV3/Xu et al. - 2019 - How Powerful are Graph Neural Networks.pdf;/home/polarolouis/Zotero/storage/ZJF5UWIH/1810.html} } +@article{yangDeepLatentSpace2024, + title = {A {{Deep Latent Space Model}} for {{Graph Representation Learning}}}, + author = {Yang, Hanxuan and Kong, Qingchao and Mao, Wenji}, + date = {2024-04}, + journaltitle = {Neurocomputing}, + volume = {576}, + eprint = {2106.11721}, + eprinttype = {arxiv}, + eprintclass = {cs, stat}, + pages = {127342}, + issn = {09252312}, + doi = {10.1016/j.neucom.2024.127342}, + url = {http://arxiv.org/abs/2106.11721}, + urldate = {2024-05-20}, + abstract = {Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from impracticability or lack interpretability, thus combined models for undirected graphs have been proposed to overcome the weaknesses. As a large portion of real-world graphs are directed graphs (of which undirected graphs are special cases), in this paper, we propose a Deep Latent Space Model (DLSM) for directed graphs to incorporate the traditional latent variable based generative model into deep learning frameworks. Our proposed model consists of a graph convolutional network (GCN) encoder and a stochastic decoder, which are layer-wise connected by a hierarchical variational auto-encoder architecture. By specifically modeling the degree heterogeneity using node random factors, our model possesses better interpretability in both community structure and degree heterogeneity. For fast inference, the stochastic gradient variational Bayes (SGVB) is adopted using a non-iterative recognition model, which is much more scalable than traditional MCMC-based methods. The experiments on real-world datasets show that the proposed model achieves the state-of-the-art performances on both link prediction and community detection tasks while learning interpretable node embeddings. The source code is available at https://github.com/upperr/DLSM.}, + langid = {english}, + keywords = {Computer Science - Machine Learning,Statistics - Machine Learning}, + file = {/home/polarolouis/Zotero/storage/XNVMI2D7/Yang et al. - 2024 - A Deep Latent Space Model for Graph Representation.pdf} +} + @online{yumpu.comInsectPollinatorsMer, title = {Insect Pollinators of the {{Mer Bleue}} Peat Bog of {{Ottawa}} - {{Biodiversity}} ...}, author = {Yumpu.com},

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