From d7ebb53a17a1e2cd309bdd7f09c1ff5751a20df6 Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Wed, 17 Jul 2024 22:46:12 +0200 Subject: [PATCH] rapport : various updates --- rapport/chapter2-context.tex | 3 +- rapport/chapter3-structure-detection.tex | 14 +++++++-- rapport/chapter4-simulation-studies.tex | 2 +- rapport/conclusions.tex | 3 ++ rapport/rapport.tex | 38 +++++++++++++----------- rapport/remerciements.tex | 6 ++-- 6 files changed, 41 insertions(+), 25 deletions(-) create mode 100644 rapport/conclusions.tex diff --git a/rapport/chapter2-context.tex b/rapport/chapter2-context.tex index 718f07b..23aaf88 100644 --- a/rapport/chapter2-context.tex +++ b/rapport/chapter2-context.tex @@ -137,7 +137,8 @@ On \ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong to the row block of corresponding color, $\bm{\rho}$ are the probabilities for a column node to belong to the column block of corresponding color and $\bm{\alpha}$ is a matrix $Q_1 \times Q_2$ of the connectivity parameters -between the row and column blocks. +between the row and column blocks. When we talk about the \enquote{structure} +of the network we are referring to this connectivity matrix. This model can be used to easily generate bipartite graphs with complex and very varied structures. But when trying to determine the structure of a given diff --git a/rapport/chapter3-structure-detection.tex b/rapport/chapter3-structure-detection.tex index 4222875..d051296 100644 --- a/rapport/chapter3-structure-detection.tex +++ b/rapport/chapter3-structure-detection.tex @@ -15,9 +15,10 @@ BiSBM for each network of the collection. For network $m$, let $n_1^m$ (resp. $n_2^m$) be the number of nodes in row (resp. column) divided into $Q_1^m$ row clusters (resp. $Q_2^m$ column -clusters).\\ Let $Z^m~=~(Z^m_i, \dots, Z^m_{n_1^m})$ and $W^m~=~(W^m_j, \dots, - W^m_{n_2^m})$ be independent latent variables such that $Z^m_i = q$ if row node -$i$ of network $m$ belongs to row cluster $q$ ($q\in\{1,\dots,Q_1^m\}$) and +clusters).\\ Let $Z^m=(Z^m_1, \dots, Z^m_i, \dots, Z^m_{n_1^m})$ and +$W^m = (W^m_1, \dots,W^m_j, \dots, W^m_{n_2^m})$ be independent latent variables +such that $Z^m_i = q$ if row node $i$ of network $m$ belongs to row cluster $q$ +($q\in\{1,\dots,Q_1^m\}$) and $W^m_j = r$ if column node $j$ of network $m$ belong to column block $r$ ($r\in\{1,\dots,Q_2^m\}$). And we have \begin{align}\label{eqn:lbm-block-membership-prob} @@ -749,3 +750,10 @@ $G_1$ and $G_2$. Else we return $\mathcal{G}$. We illustrate our capacity to perform a partition of a collection for all colBiSBM models in %\ref{sec:network-clustering-of-simulated-networks}. + +\section{Model identifiability} +\label{sec:model-identifiability} + +% Ici l'identifiabilité du modèle + +\cite{chabert-liddellLearningCommonStructures2024a,celisseConsistencyMaximumlikelihoodVariational2012,keribinEstimationSelectionLatent2015} \ No newline at end of file diff --git a/rapport/chapter4-simulation-studies.tex b/rapport/chapter4-simulation-studies.tex index 3dfab71..3a24440 100644 --- a/rapport/chapter4-simulation-studies.tex +++ b/rapport/chapter4-simulation-studies.tex @@ -7,7 +7,7 @@ performances and the clustering capacities. \paragraph{Reproducibility} All the codes used to obtain data and to perform the analysis can be found on the report repository at -\url{https://gitea.polarolouis.fr/polarolouis/rapport-CEI-MIA-2023}. +\url{https://gitea.polarolouis.fr/polarolouis/mia-stage-2024}. \input{chapter4-simulations/inference} diff --git a/rapport/conclusions.tex b/rapport/conclusions.tex new file mode 100644 index 0000000..c53af71 --- /dev/null +++ b/rapport/conclusions.tex @@ -0,0 +1,3 @@ +\addtocounter{customchapter}{1} +\chapter{Conclusions and future work} +\label{chap:conclusions-and-future-work} \ No newline at end of file diff --git a/rapport/rapport.tex b/rapport/rapport.tex index 2d7abd0..6c9e2f5 100644 --- a/rapport/rapport.tex +++ b/rapport/rapport.tex @@ -211,29 +211,31 @@ automata,positioning} % Pour activer les onglets \ActivateBG \begin{selectlanguage}{french} - % \maketitle - \pagenumbering{roman} - \tableofcontents - \include{remerciements} - % \include{chapter1-presentation_UMR} + % \maketitle + \pagenumbering{roman} + \tableofcontents + \include{remerciements} + % \include{chapter1-presentation_UMR} \end{selectlanguage} \begin{selectlanguage}{english} - \pagenumbering{arabic} - \include{chapter2-context} - \include{chapter3-structure-detection} - \include{chapter4-simulation-studies} + \pagenumbering{arabic} + \include{chapter2-context} + \include{chapter3-structure-detection} + \include{chapter4-simulation-studies} - % \chapter{Applications} - % \include{Rcodes/real_data/application_dore} - % \include{Rcodes/real_data/CoOPLBM_completion_analyze} + % \chapter{Applications} + % \include{Rcodes/real_data/application_dore} + % \include{Rcodes/real_data/CoOPLBM_completion_analyze} - \addtocounter{maincontentend}{1} - \addtocounter{customchapter}{1} - \printbibliography - \input{appendices.tex} - % \listoffigures - % \listoftables + \include{conclusions} + + \addtocounter{maincontentend}{1} + \addtocounter{customchapter}{1} + \printbibliography + \input{appendices.tex} + % \listoffigures + % \listoftables \end{selectlanguage} \end{document} diff --git a/rapport/remerciements.tex b/rapport/remerciements.tex index 298e91e..fcdf7f2 100644 --- a/rapport/remerciements.tex +++ b/rapport/remerciements.tex @@ -13,9 +13,11 @@ Merci à Farida, Christelle et Sébastien pour avoir expliqué et mené les démarches administratives. Un merci tout particulier à tous les doctorants : Mary, -Marina, Emré, Tam, Caroline, Jérémy, Florian, Annaïg, Jules, Hayato, Tanguy, Barbara, +Marina, Emré, Tam, Caroline, Jérémy, Florian, Annaïg, Jules, Hayato, Jeanne, +Tanguy, Barbara, Bastien et Armand. Merci à tous les autres stagiaires, particulièrement: -Alizée, Taliesin, Antoine, Alexandre, Francois, Pierre, Camille et Maxime. +Alizée, Taliesin, Antoine, Alexandre, Francois, Vincent, Pierre, Camille et +Maxime. Merci à tous les permanents du 3\ieme étage, parmi lesquels: Christophe, Stéphane et Vincent.