795 lines
37 KiB
TeX
795 lines
37 KiB
TeX
\section{Parcours}
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||
\label{sec:parcours}
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||
\begin{frame}{Formations}
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||
|
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\begin{itemize}
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\item 2018--2020, Classe Préparatoire BCPST
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\item 2020--2022, 1ère et 2ème année en formation Ingénieur
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||
AgroParisTech\\
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{\small Cours optionnels suivis : statistiques spatiales,
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mathématiques pour la santé, ingénierie par la simulation informatique \dots}
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\item 2022--2023, Année de césure
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\item 2023--2024, M2 Mathématiques pour les Sciences du Vivant,
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Université Paris-Saclay\\
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{\small UC à choix 2\ieme semestre : modèles à variables
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latentes, statistiques spatiales et méthodes de statistiques en grandes dimension}
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\end{itemize}
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\end{frame}
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\begin{frame}{Expériences professionnelles}
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\begin{itemize}
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\item 2022 Mai--Déc., Stage assistant ingénieur en Qualité chez
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Eurofins Food France
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\item 2023 Janv.--Juillet, Détection de structures dans des collections de
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réseaux bipartites et écriture du package implémentant la méthode.
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Stage dans l’UMR MIA Paris-Saclay, supervisé par Pierre Barbillon.
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\item 2024 Avril--Sept., Détection de structures et clustering de réseaux
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écologiques. Stage dans l’UMR MIA Paris-Saclay, supervisé par
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Pierre Barbillon et Sophie Donnet.
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||
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\end{itemize}
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||
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\end{frame}
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\section{Sujet de thèse}
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\begin{frame}
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\frametitle{Contexte écologique}
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\begin{itemize}
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\item Nombreux réseaux disponibles \parencite{WebLifeEcological} pour interactions similaires. Par exemple,
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interactions proies-prédateurs, plantes-pollinisateurs \dots
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\item Suivi biodiversité, analyse de robustesse et risque d'effondrement
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% Ces réseaux permettent un suivi de la biodiversité, de détecter
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% et d'analyser la robustesse et les changements subies par ces
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% écosystèmes et notamment les risques d'effondrement de la
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% biodiversité.
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\begin{figure}[ht]
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\centering
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\begin{tikzpicture}[scale=.6]
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\tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,thin,draw]
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\tikzstyle{every state}=[draw, text=white,scale=0.65, font=\scriptsize, transform shape]
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% Upper level
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\tikzstyle{every state}=[draw=none,text=white,scale=0.55, font=\scriptsize, transform shape]
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% premier cluster
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\tikzstyle{every node}=[fill=green!50!blue!20!white]
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\node[state] (N1) at (1.1,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}};
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\node[state, right = of N1] (N2) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (.75,3)
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\node[state, right = of N2] (N3) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (1.5,3)
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\node[state, right = of N3] (N4) {\includegraphics[width=.1\textwidth]{img/pollen.png}}; % at (2.25,3)
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% \node[state] (N5) at (3,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}};
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% \node[state] (N6) at (3.75,3) {\includegraphics[width=.1\textwidth]{img/pollen.png}};
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\tikzstyle{every node}=[shape=rectangle,fill=red!50!blue!20!white]
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% \node[state, fill = white] (P) at (-1.5, 0) {\includegraphics[width=.08\textwidth]{img/bee.png}};
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\node[state, tokens=0] (P1) at (-1, 0) {\includegraphics[width=.1\textwidth]{img/bee.png}};
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\node[state, tokens=0, right = of P1] (P2) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (-.25, 0)
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\node[state, tokens=0, right = of P2] (P3) {\includegraphics[width=.1\textwidth]{img/bee.png}}; %at (.5, 0)
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\node[state, tokens=0, right = of P3] (P4) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (1.25, 0)
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\node[state, tokens=0, right = of P4] (P5) {\includegraphics[width=.1\textwidth]{img/bee.png}};% at (2,0)
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\node[state, tokens=0, right = of P5] (P6) {\includegraphics[width=.1\textwidth]{img/bee.png}}; % at (2.75,0)
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% \node[state, tokens=0] (P7) at (3.5,0) {\includegraphics[width=.1\textwidth]{img/bee.png}};
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% \node[state, tokens=0] (P8) at (4.25,0) {\includegraphics[width=.1\textwidth]{img/bee.png}};
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\tikzstyle{every edge}=[>=stealth,shorten >=1pt,auto,thin,draw]
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\path (P1) edge (N1);
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\path (P2) edge (N1);
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\path (P3) edge (N1);
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\path (P4) edge (N2);
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\path (P4) edge (N1);
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\path (P6) edge (N2);
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\path (P1) edge (N3);
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%\path (P7) edge (N4);
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%\path (P8) edge (N5);
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%\path (P4) edge (N6);
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\path (P5) edge (N3);
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\path (P5) edge (N4);
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\end{tikzpicture}
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\caption{Exemple d'un réseau plantes-pollinisateurs}
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\label{fig:plantes-pollin}
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\end{figure}
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\item En écologie microbienne réseaux permettent le suivi de la
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qualité des sols.
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% En écologie microbienne, les réseaux sont construits sur la base
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% de co-occurences et reconstruits par inférence des liens mais
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% rarement par observation directe.
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\end{itemize}
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\end{frame}
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\begin{frame}{Contexte mathématique}
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Détection de structure\footnote{L'organisation du réseau.} pour un réseau
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bien connu :
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\begin{itemize}
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\item Modèles de \emph{clustering} à variables latentes
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\item \emph{Embedding} par apprentissage profond
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\end{itemize}
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Mais des motivations pour considérer des collections :
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\begin{itemize}
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\item Espèces différentes, rôles analogues
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% Des espèces différentes dans plusieurs réseaux pourrait
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% remplir des rôles similaires
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\item Transfert d'informations grands vers petits réseaux.
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% Les petits réseaux pourraient bénéficier d'une estimation
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% avec des réseaux plus grands et révéler une structure plus
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% fine.
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% Certains réseaux étant moins bien échantillonnés que
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% d'autre une prise en compte en collection de réseaux pourrait
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% aider à transférer de l'information
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\item Regrouper les réseaux selon leur similarité (\emph{clustering}
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de réseaux)
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\end{itemize}
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\end{frame}
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\subsection[Axe 1]{Axe 1 : Modèles à variables
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latentes pour une collection de réseaux bipartites}
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\label{sec:axe-1}
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\begin{frame}
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\frametitle{Réseaux bipartites}
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\begin{columns}[c]
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\begin{column}{0.48\textwidth}
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\centering
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Réseau bipartite\\
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\begin{tikzpicture}[scale=.6]
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\tikzstyle{every edge}=[-,>=stealth',shorten
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>=1pt,auto,draw,line width=1.5pt]
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||
\tikzstyle{every state}=[draw, text=black,scale=0.95, transform
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shape]
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||
\tikzstyle{every state}=[draw=none,text=black,scale=0.75,
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transform shape]
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||
\tikzstyle{every node}=[fill=blueind]
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||
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||
\node[state, draw=black!50] (A1) at (0,5) {\textbf{R1}};
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\node[state, draw=black!50] (A2) at (2.5,5) {\textbf{R2}};
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\node[state, draw=black!50] (A3) at (5,5) {\textbf{R3}};
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||
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||
\tikzstyle{every node}=[fill=greenind, shape=rectangle]
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||
\tikzstyle{every state}=[draw=none,text=black,scale=0.75,
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transform shape, shape=rectangle]
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||
\node[state, draw=black!50] (B1) at (0,0) {\textbf{C1}};
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||
\node[state, draw=black!50] (B2) at (1.25,0) {\textbf{C2}};
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||
\node[state, draw=black!50] (B3) at (2.5,0) {\textbf{C3}};
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||
\node[state, draw=black!50] (B4) at (3.75,0) {\textbf{C4}};
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||
\node[state, draw=black!50] (B5) at (5,0) {\textbf{C5}};
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||
\path (A1) edge [] (B1);
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||
\path (A1) edge (B2);
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||
\path (A1) edge (B3);
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||
\path (A1) edge (B4);
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||
\path (A2) edge (B3);
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||
\path (A2) edge (B4);
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||
\path (A3) edge (B5);
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\path (A2) edge (B5);
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\end{tikzpicture}
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\end{column}
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\hfill
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\begin{column}{0.48\linewidth}
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Matrice d'incidence
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\smallskip
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$X=\left(
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\begin{array}{rrrrr}
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1 & 1 & 1 & 1 & 0 \\
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0 & 0 & 1 & 1 & 1 \\
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0 & 0 & 0 & 0 & 1 \\
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\end{array}\right)
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$\\
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\end{column}
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\end{columns}
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\smallskip
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Décrit des interactions (pas uniquement binaires) entre deux groupes d'agents :
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\begin{itemize}
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\item hôtes-parasites
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\item plantes-pollinisateurs
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\item graines-disperseurs\newline
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\vdots
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\end{itemize}
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\end{frame}
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\begin{frame}
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\frametitle{Latent Block Model (LBM)}
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Proposé par~\cite{govaertEMAlgorithmBlock2005}.
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\begin{columns}
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\begin{column}{0.40\linewidth}
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\begin{figure}[H]
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||
\center
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||
\begin{tikzpicture}[scale=0.35]
|
||
\tikzstyle{every state}=[draw, text=black,scale=0.95,
|
||
transform shape]
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||
\tikzstyle{every state}=[draw=none,text=black,scale=0.75,
|
||
transform shape]
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||
\tikzset{edge_proba/.style={draw=white, fill=none,
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||
text=black}}
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||
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||
\tikzstyle{every node}=[fill=blueind]
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||
\node[edge_proba] (pi1) at (1,5.7)
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||
{\textbf{$\pi_{{\color{blueind}\bullet}}$}};
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||
\node[state, draw=black!50] (R11) at (0,5) {\textbf{R11}};
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||
\node[state, draw=black!50] (R12) at (1,5) {\textbf{R12}};
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||
\node[state, draw=black!50] (R13) at (2,5) {\textbf{R13}};
|
||
|
||
\tikzstyle{every node}=[fill=cyanind]
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||
\node[edge_proba] (pi2) at (6.75,5.7)
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||
{\textbf{$\pi_{{\color{cyanind}\bullet}}$}};
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||
\node[state, draw=black!50] (R21) at (6.25,5)
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||
{\textbf{R21}};
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||
\node[state, draw=black!50] (R22) at (7.25,5)
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||
{\textbf{R22}};
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||
|
||
\tikzstyle{every node}=[fill=electricblue]
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||
\node[edge_proba] (pi3) at (10,5.7)
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||
{\textbf{$\pi_{{\color{electricblue}\bullet}}$}};
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||
\node[state, draw=black!50] (R31) at (10,5) {\textbf{R31}};
|
||
|
||
\tikzstyle{every node}=[fill=burntorange, shape=rectangle]
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||
\node[edge_proba] (pi3) at (0.5,-0.7)
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||
{\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,
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||
fill=none] {$\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}}$}
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||
(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}
|
||
\frametitle{Collections bipartites}
|
||
\begin{center}
|
||
\begin{adjustbox}{trim=0 0 1 1.5cm}
|
||
\begin{tikzpicture}[scale=.33]
|
||
\begin{scope}[xshift=18cm, yshift=2cm]
|
||
\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] (rho1) at (0.5,-1)
|
||
{\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] (rho2) at (4,-1)
|
||
{\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] (rho3) at (10,-1)
|
||
{\textbf{$\rho_{{\color{peach}\bullet}}$}};
|
||
\node[state, draw=black!50] (B5) at (10,0) {\textbf{C31}};
|
||
|
||
\node[font=\small, text justified,draw=none, fill=none,
|
||
below = 0.05cm of rho2] {LBM};
|
||
|
||
\tikzstyle{every edge}=[-,>=stealth',shorten
|
||
>=1pt,auto,draw,line width=1.5pt,draw opacity=0.2]
|
||
|
||
\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 (R21) edge (B4);
|
||
\path (R21) edge (B5);
|
||
|
||
\path (R22) edge (B3);
|
||
\path (R22) edge (B4);
|
||
|
||
\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 (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,
|
||
anchor=center, fill=none]
|
||
{$\alpha_{{\color{cyanind}\bullet}{\color{goldenyellow}\bullet}}$} (B3);
|
||
\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{scope}
|
||
|
||
\begin{scope}[xshift=3cm, yshift = 1cm]
|
||
\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]
|
||
|
||
\tikzstyle{every node}=[fill=gray]
|
||
\node[state, draw=black!50] (R11) at (0,1.25)
|
||
{\textbf{1}};
|
||
\node[state, draw=black!50] (R12) at (1,1.25)
|
||
{\textbf{2}};
|
||
\node[state, draw=black!50] (R13) at (2,1.25)
|
||
{\textbf{3}};
|
||
\node[state, draw=black!50] (R21) at (3,1.25)
|
||
{\textbf{4}};
|
||
\node[state, draw=black!50] (R31) at (5,1.25)
|
||
{\textbf{6}};
|
||
|
||
\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 = $};
|
||
|
||
|
||
\node[state, draw=black!50] (B1) at (0.5,-1)
|
||
{\textbf{1}};
|
||
|
||
\node[state, draw=black!50] (B31) at (2.5,-1)
|
||
{\textbf{3}};
|
||
\node[state, draw=black!50] (B4) at (3.5,-1)
|
||
{\textbf{4}};
|
||
|
||
\node[state, draw=black!50] (B5) at (4.5,-1)
|
||
{\textbf{5}};
|
||
|
||
\tikzstyle{every edge}=[-,>=stealth',shorten
|
||
>=1pt,auto,draw,line width=1pt, draw=gray, fill=gray]
|
||
\path (R11) edge (B1);
|
||
\path (R11) edge (B31);
|
||
\path (R11) edge (B4);
|
||
|
||
\path (R12) edge [] (B1);
|
||
\path (R12) edge (B31);
|
||
\path (R12) edge (B4);
|
||
|
||
\path (R13) edge [] (B1);
|
||
\path (R13) edge (B31);
|
||
\path (R13) edge (B4);
|
||
|
||
\path (R21) edge (B31);
|
||
\path (R21) edge (B4);
|
||
\path (R21) edge (B5);
|
||
|
||
\path (R31) edge (B5);
|
||
\end{scope}
|
||
\node[text width=3cm,font=\small, text justified,
|
||
rotate=90, fill=none] (dots) at (2.5, 7.5){\dots};
|
||
|
||
\begin{scope}[yshift = 0cm]
|
||
\tikzstyle{every state}=[draw, text=black,scale=0.75,
|
||
transform shape]
|
||
|
||
\tikzstyle{every node}=[fill=gray]
|
||
\node[state, draw=black!50] (R11) at (0,2.25)
|
||
{\textbf{4}};
|
||
\node[state, draw=black!50] (R13) at (2,2.25)
|
||
{\textbf{6}};
|
||
\node[state, draw=black!50] (R21) at (3,2.25)
|
||
{\textbf{3}};
|
||
\node[state, draw=black!50] (R22) at (4,2.25)
|
||
{\textbf{5}};
|
||
\node[state, draw=black!50] (R31) at (5,2.25)
|
||
{\textbf{2}};
|
||
|
||
\tikzstyle{every
|
||
state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle]
|
||
% Label réseau
|
||
\node[font=\small, text justified,draw=none, fill=none,
|
||
below left = 0.04cm of R11] {$Y^M = $};
|
||
|
||
\node[state, draw=black!50] (B1) at (0.5,0)
|
||
{\textbf{5}};
|
||
\node[state, draw=black!50] (B2) at (1.5,0)
|
||
{\textbf{1}};
|
||
|
||
\node[state, draw=black!50] (B4) at (3.5,0)
|
||
{\textbf{2}};
|
||
|
||
\node[state, draw=black!50] (B5) at (4.5,0)
|
||
{\textbf{4}};
|
||
|
||
\tikzstyle{every edge}=[-,>=stealth',shorten
|
||
>=1pt,auto,draw,line width=1pt, draw=gray, fill=gray]
|
||
\path (R11) edge (B1);
|
||
\path (R11) edge (B2);
|
||
\path (R11) edge (B4);
|
||
|
||
\path (R13) edge [] (B1);
|
||
\path (R13) edge (B2);
|
||
\path (R13) edge (B4);
|
||
|
||
\path (R21) edge (B4);
|
||
\path (R21) edge (B5);
|
||
|
||
\path (R22) edge (B4);
|
||
\path (R22) edge (B5);
|
||
|
||
\path (R31) edge (B5);
|
||
\end{scope}
|
||
\end{scope}
|
||
\end{tikzpicture}
|
||
\end{adjustbox}
|
||
\end{center}
|
||
|
||
\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 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}
|
||
|
||
\end{frame}
|
||
|
||
\begin{frame}
|
||
\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}
|
||
|
||
\begin{center}
|
||
\begin{table}
|
||
\tiny
|
||
\begin{tabular}{ |c|c|c|c|c|c| }
|
||
\hline
|
||
\thead{N°de \\collection} & 1 & 2 & 3 & 4 & 5 \\
|
||
\hline
|
||
\thead{Nombre de \\réseaux} & 38 & 45 & 1 & 20 & 19 \\
|
||
\hline
|
||
\end{tabular}
|
||
\end{table}
|
||
|
||
\end{center}
|
||
\end{column}
|
||
\end{columns}
|
||
\end{frame}
|
||
|
||
\begin{frame}{À faire}
|
||
\begin{itemize}
|
||
\item Finaliser l'analyse sur données réelles
|
||
commencée sur \cite{doreRelativeEffectsAnthropogenic2021,
|
||
thebaultDatabasePlantpollinatorNetworks2020} avec les
|
||
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{frame}
|
||
|
||
\subsection[Axe 2]{Axe 2 : Embedding de n\oe uds par
|
||
apprentissage profond pour comparaison des topologies de réseaux}
|
||
\label{sec:axe-2}
|
||
|
||
\begin{frame}[allowframebreaks]{\emph{Graph Neural Networks}}
|
||
\begin{figure}
|
||
\includegraphics[scale=0.4]{img/Message_passing.pdf}
|
||
\caption{Illustration du \emph{message passing} au sein d'un graphe.\footnote{Figure adaptée de \cite{sanchez-lengelingGentleIntroductionGraph2021} par Emré Anakok.}}
|
||
\end{figure}
|
||
|
||
|
||
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}.
|
||
\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.\\
|
||
|
||
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}
|
||
|
||
\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}
|
||
\section{Organisation de la thèse}
|
||
\label{sec:organisation-these}
|
||
|
||
\begin{frame}
|
||
\begin{block}{Planning prévisionnel de la thèse}
|
||
\begin{figure}[ht]
|
||
\centering
|
||
\begin{chronology}[1]{2024}{2028}{\textwidth}[110ex]
|
||
\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}{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]
|
||
% \eventpoint{\decimaldate{11}{4}{1976}}{Launch of Apple I}[red][1][1]
|
||
% \eventpoint{\decimaldate{12}{8}{1981}}{Launch of IBM PC}[red][1][1]
|
||
% \eventpoint{\decimaldate{15}{9}{1993}}{Debian 0.01}[red][1][1]
|
||
% \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}
|
||
\caption{Chronologie prévue}
|
||
\label{fig:chronologie}
|
||
\end{figure}
|
||
|
||
% \begin{itemize}
|
||
% \item Axe 1 : Oct. 2024 -- Oct. 2025
|
||
% \item Axe 2 : Oct. 2025 -- Oct. 2026
|
||
% \item Axe 3 : Avril 2026 -- Octobre 2027
|
||
% \item Rédaction du manuscrit de thèse : Avril 2027 -- Octobre 2027
|
||
% \end{itemize}
|
||
\end{block}
|
||
\begin{block}{Financement}
|
||
L'INRAE, par le département MathNum accorde déjà 50\% des financements
|
||
de la thèse.
|
||
\end{block}
|
||
\end{frame}
|
||
|
||
\begin{frame}[noframenumbering]
|
||
\vfill
|
||
\centering
|
||
\huge Merci pour votre attention.
|
||
\vfill
|
||
\end{frame}
|