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- \tikzstyle{every node}=[fill=blueind] - - \node[state, draw=black!50] (A1) at (0,5) {\textbf{R1}}; - \node[state, draw=black!50] (A2) at (2.5,5) {\textbf{R2}}; - \node[state, draw=black!50] (A3) at (5,5) {\textbf{R3}}; - - \tikzstyle{every node}=[fill=greenind, shape=rectangle] - \tikzstyle{every state}=[draw=none,text=black,scale=0.75, - transform shape, shape=rectangle] - \node[state, draw=black!50] (B1) at (0,0) {\textbf{C1}}; - \node[state, draw=black!50] (B2) at (1.25,0) {\textbf{C2}}; - \node[state, draw=black!50] (B3) at (2.5,0) {\textbf{C3}}; - \node[state, draw=black!50] (B4) at (3.75,0) {\textbf{C4}}; - \node[state, draw=black!50] (B5) at (5,0) {\textbf{C5}}; - \path (A1) edge [] (B1); - \path (A1) edge (B2); - \path (A1) edge (B3); - \path (A1) edge (B4); - \path (A2) edge (B3); - \path (A2) edge (B4); - \path (A3) edge (B5); - \path (A2) edge (B5); - \end{tikzpicture} - \end{column} - \hfill - \begin{column}{0.48\linewidth} - Matrice d'incidence - \smallskip - $X=\left( - \begin{array}{rrrrr} - 1 & 1 & 1 & 1 & 0 \\ - 0 & 0 & 1 & 1 & 1 \\ - 0 & 0 & 0 & 0 & 1 \\ - \end{array}\right) - $\\ - \end{column} - \end{columns} - \smallskip - 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}. @@ -565,86 +506,22 @@ \begin{itemize} \item Écriture du modèle colBiSBM \item Dérivation des formules d'inférence et d'un critère de sélection - de modèle de vraisemblance pénalisée + de modèle par vraisemblance pénalisée (choix du nombre de blocs). \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. + \note[item]{Principalement pendant mon premier stage} + \item Développement d'une méthode de partitionnement d'une large + collection de réseaux basée sur la maximisation d'un critère de + sélection de modèle. \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} + \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 @@ -684,21 +561,21 @@ \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.} + \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{itemize} \end{frame} @@ -706,47 +583,166 @@ apprentissage profond pour comparaison des topologies de réseaux} \label{sec:axe-2} -\begin{frame}[allowframebreaks]{\emph{Graph Neural Networks}} +% % \begin{tikzpicture}[ +% % vertex/.style = {circle, draw, inner sep=0.5pt, fill=white}, +% % vertex1/.style = {vertex, fill=red!30!white}, +% % vertex2/.style = {vertex, fill=orange!30!white}, +% % vertex3/.style = {vertex, fill=blue!30!white}, +% % vertex4/.style = {vertex, fill=teal!30!white}, +% % scale = 0.5 +% % ] +% % \begin{scope} +% % \draw[thick] +% % (-0.5,0) node[vertex1] (n1^4) {$n_1$} +% % -- (0.25,2.2) node[vertex2] (n2^4) {$n_2$} +% % -- (2,1.6) node[vertex3] (n3^4) {$n_3$} +% % -- (-0.7,1.4) node[vertex4] (n4^4) {$n_4$} -- cycle; +% % \node[left = 0.15cm of n4^4, fill = white] {$Y^m$}; +% % \end{scope} +% % \end{tikzpicture} + + +\begin{frame}{Introduction aux \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.}} + \centering + % \begin{tikzpicture}[ + % % node distance=2cm and 1cm, + % trap/.style={trapezium, draw, minimum height = 1cm}, + % % rectangle/.style={rectangle, draw, minimum height=1cm, minimum width=2cm, align=center}, + % arrow/.style={->, thick}, + % scale=0.5, + % ] + + % % Encoder trapezium + % \node[trap, trapezium left angle=110, trapezium right angle=110, rotate = 90] (encoder) {Encodeur}; + + % % Latent space parameters + % \node[rectangle, fill=yellow, opacity=0.4, below=of encoder] (mu) {$\mu$}; + % \node[rectangle, fill=blue, opacity=0.3, below=of mu] (sigma) {$\sigma$}; + % \node[rectangle, fill=green, opacity=0.3, below=of sigma, rotate = 90] (sample) {Échantillon}; + + % % Decoder trapezium + % \node[trap, trapezium left angle=70, trapezium right angle=70, below=of sample, rotate = 90] (decoder) {Décodeur}; + + % % Connections + % \draw[arrow] (encoder.south) -- (mu.north); + % \draw[arrow] (encoder.south) -- (sigma.north); + % \draw[arrow] (mu.south) -- (sample.north); + % \draw[arrow] (sigma.south) -- (sample.north); + % \draw[arrow] (sample.south) -- (decoder.north); + + % % Input and output labels + % \node[left= 2cm of encoder] (input) {Input $x$}; + % \node[right= 2cm of decoder] (output) {Output $\hat{x}$}; + + % \draw[arrow] (input.east) -- (encoder.west); + % \draw[arrow] (decoder.east) -- (output.west); + + % \end{tikzpicture} + \includegraphics[scale=0.20]{img/vae.png} + \caption{Schéma d'\cite{AutoencodeurVariationnel2024}} + \label{fig:schema-vgae} \end{figure} + \footnotesize + Problème des graphes pour les réseaux de neurones : \textbf{prise en compte + des invariances}. - - 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. + \item Utilisation des \emph{Graph Convolutional Networks} de + \cite{kipfSemiSupervisedClassificationGraph2017} résout ce problème. + \item Utiliser des \emph{Variational AutoEncoder} de + \cite{kingmaAutoEncodingVariationalBayes2022c} et de + \cite{kipfVariationalGraphAutoEncoders2016} pour projection dans un + espace latent. + \item Explorer le \emph{Deep Latent Space Model} + de~\cite{yangDeepLatentSpace2024} \end{itemize} \end{frame} +\begin{frame}{Idées à explorer} + \begin{itemize} + \item \emph{Embedding} commun des n\oe uds des réseaux à comparer sur un même espace + latent. Puis comparaison des distributions ainsi obtenues. + \item Encodeurs différents mais décodeurs communs pour comparer les + représentations obtenues + \end{itemize} + + Ces pistes seront approfondies durant ce travail de thèses + +\end{frame} + +% \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. + \begin{columns} + \begin{column}{0.4\textwidth} + \begin{table}[t] + \centering + \begin{tabularx}{\textwidth}{cccc} + \hline + & \multicolumn{3}{|c|}{OTU} \\ + \hline + & $X_{1,1}$ & \dots & $X_{1,p}$ \\ + & \vdots & & \vdots \\ + & $X_{n,1}$ & \dots & $X_{n,p}$ \\ + \hline + \end{tabularx} + \caption{Table d'OTU synthétique} + \label{tab:otu-synthetiques} + \end{table} + \end{column} - Limites des techniques actuelles \cite{matchadoNetworkAnalysisMethods2021}. - Rôle important pour les réseaux reconstruits notamment en microbiologie. + \begin{column}{0.6\textwidth} + \begin{figure}[t] + \centering + \includegraphics[scale=0.25]{img/plot_model_function_eps.png} + \caption{Réseau inféré} + \label{fig:otu-synthetiques} + \end{figure} + \end{column} + \end{columns}. + + \begin{itemize} + \item Incertitude disponible mais négligée par la suite + \item Important pour les réseaux microbiens seulement inférés + \end{itemize} + \cite{matchadoNetworkAnalysisMethods2021} + \end{frame} + \section{Organisation de la thèse} \label{sec:organisation-these} @@ -763,33 +759,15 @@ {\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} + \Large Merci pour votre attention. +\end{frame} \ No newline at end of file diff --git a/references.bib b/references.bib index 0979191..bba53bf 100644 --- a/references.bib +++ b/references.bib @@ -39,6 +39,18 @@ file = {/home/polarolouis/Zotero/storage/A4V9MJAF/Aubert et al. - 2021 - Model-based biclustering for overdispersed count d.pdf} } +@inreference{AutoencodeurVariationnel2024, + title = {Auto-encodeur variationnel}, + booktitle = {Wikipédia}, + date = {2024-03-13T19:44:29Z}, + url = {https://fr.wikipedia.org/w/index.php?title=Auto-encodeur_variationnel&oldid=213326719}, + urldate = {2024-05-21}, + abstract = {En apprentissage automatique, un auto-encodeur variationnel (ou VAE de l'anglais variational auto encoder), est une architecture de réseau de neurones artificiels introduite en 2013 par D. Kingma et M. Welling, appartenant aux familles des modèles graphiques probabilistes et des méthodes bayésiennes variationnelles. Les VAE sont souvent rapprochés des autoencodeurs, en raison de leur architectures similaires. Leur utilisation et leur formulation mathématiques sont cependant différentes. Les auto-encodeurs variationnels permettent de formuler un problème d'inférence statistique (par exemple, déduire la valeur d'une variable aléatoire à partir d'une autre variable aléatoire) en un problème d'optimisation statistique (c'est-à-dire trouver les valeurs de paramètres qui minimisent une fonction objectif). Ils représentent une fonction associant à une valeur d'entrée une distribution latente multivariée, qui n'est pas directement observée mais déduite depuis un modèle mathématique à partir de la distribution d'autres variables. Bien que ce type de modèle ait été initialement conçu pour l'apprentissage non supervisé, son efficacité a été prouvée pour l'apprentissage semi-supervisé, et l'apprentissage supervisé.}, + langid = {french}, + annotation = {Page Version ID: 213326719}, + file = {/home/polarolouis/Zotero/storage/HLPG5K7Y/Auto-encodeur_variationnel.html} +} + @online{battagliaRelationalInductiveBiases2018, title = {Relational Inductive Biases, Deep Learning, and Graph Networks}, author = {Battaglia, Peter W. and Hamrick, Jessica B. and Bapst, Victor and Sanchez-Gonzalez, Alvaro and Zambaldi, Vinicius and Malinowski, Mateusz and Tacchetti, Andrea and Raposo, David and Santoro, Adam and Faulkner, Ryan and Gulcehre, Caglar and Song, Francis and Ballard, Andrew and Gilmer, Justin and Dahl, George and Vaswani, Ashish and Allen, Kelsey and Nash, Charles and Langston, Victoria and Dyer, Chris and Heess, Nicolas and Wierstra, Daan and Kohli, Pushmeet and Botvinick, Matt and Vinyals, Oriol and Li, Yujia and Pascanu, Razvan}, @@ -158,6 +170,23 @@ file = {/home/polarolouis/Zotero/storage/4USKD3WW/Chabert-Liddell et al. - 2024 - Learning common structures in a collection of netw.pdf} } +@article{daigavaneUnderstandingConvolutionsGraphs2021, + title = {Understanding {{Convolutions}} on {{Graphs}}}, + author = {Daigavane, Ameya and Ravindran, Balaraman and Aggarwal, Gaurav}, + date = {2021-09-02}, + journaltitle = {Distill}, + volume = {6}, + number = {9}, + pages = {e32}, + issn = {2476-0757}, + doi = {10.23915/distill.00032}, + url = {https://distill.pub/2021/understanding-gnns}, + urldate = {2024-05-21}, + abstract = {Understanding the building blocks and design choices of graph neural networks.}, + langid = {english}, + file = {/home/polarolouis/Zotero/storage/RBH4EXGY/understanding-gnns.html} +} + @article{daudinMixtureModelRandom2008, title = {A Mixture Model for Random Graphs}, author = {Daudin, J.-J. and Picard, F. and Robin, S.}, @@ -361,6 +390,22 @@ file = {/home/polarolouis/Zotero/storage/49IKUHMA/s11222-014-9472-2.pdf.pdf;/home/polarolouis/Zotero/storage/VXKAK359/Keribin et al. - 2015 - Estimation and selection for the latent block mode.pdf} } +@online{kingmaAutoEncodingVariationalBayes2022c, + title = {Auto-{{Encoding Variational Bayes}}}, + author = {Kingma, Diederik P. and Welling, Max}, + date = {2022-12-10}, + eprint = {1312.6114}, + eprinttype = {arxiv}, + eprintclass = {cs, stat}, + doi = {10.48550/arXiv.1312.6114}, + url = {http://arxiv.org/abs/1312.6114}, + urldate = {2024-05-21}, + abstract = {How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions are two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.}, + pubstate = {preprint}, + keywords = {Computer Science - Machine Learning,Statistics - Machine Learning}, + file = {/home/polarolouis/Zotero/storage/ECSHPY3J/Kingma et Welling - 2022 - Auto-Encoding Variational Bayes.pdf;/home/polarolouis/Zotero/storage/MK5TFH4E/1312.html} +} + @online{kipfSemiSupervisedClassificationGraph2017, title = {Semi-{{Supervised Classification}} with {{Graph Convolutional Networks}}}, author = {Kipf, Thomas N. and Welling, Max},