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<h1 class="title">Bilan semaine 51 2025 : 15 décembre - 19 décembre</h1>
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<div class="quarto-categories">
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<div class="quarto-category">colBiSBM</div>
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<div class="quarto-category">inférence</div>
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<div class="quarto-category">GNN</div>
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<div class="quarto-title-meta-heading">Auteur·rice</div>
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<div class="quarto-title-meta-heading">Affiliation</div>
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<div class="quarto-title-meta-contents">
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<p class="author">Louis Lacoste <a href="mailto:louis.lacoste@agroparistech.fr" class="quarto-title-author-email"><i class="bi bi-envelope"></i></a> <a href="https://orcid.org/0009-0004-0178-9821" class="quarto-title-author-orcid"> <img src="data:image/png;base64,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"></a></p>
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<div class="quarto-title-meta-contents">
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<p class="affiliation">
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MIA Paris-Saclay, INRAE, AgroParisTech, Université Paris-Saclay
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<div class="quarto-title-meta-heading">Date de publication</div>
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<p class="date">19 décembre 2025</p>
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<div class="quarto-title-meta-heading">Modifié</div>
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<p class="date-modified">11 mai 2026</p>
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<h2 id="toc-title">Sur cette page</h2>
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<ul>
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<li><a href="#todo-list" id="toc-todo-list" class="nav-link active" data-scroll-target="#todo-list"><span class="header-section-number">1</span> TODO List</a>
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<ul class="collapse">
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<li><a href="#inférence-et-microbes" id="toc-inférence-et-microbes" class="nav-link" data-scroll-target="#inférence-et-microbes"><span class="header-section-number">1.1</span> Inférence et microbes</a></li>
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</ul></li>
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<li><a href="#a-discuter" id="toc-a-discuter" class="nav-link" data-scroll-target="#a-discuter"><span class="header-section-number">2</span> A discuter</a></li>
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<li><a href="#biblio-à-faire" id="toc-biblio-à-faire" class="nav-link" data-scroll-target="#biblio-à-faire"><span class="header-section-number">3</span> Biblio à faire</a></li>
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<li><a href="#lectures-en-cours" id="toc-lectures-en-cours" class="nav-link" data-scroll-target="#lectures-en-cours"><span class="header-section-number">4</span> Lectures en cours 📚</a>
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<li><a href="#hdr-vincent-brault" id="toc-hdr-vincent-brault" class="nav-link" data-scroll-target="#hdr-vincent-brault"><span class="header-section-number">4.1</span> HDR Vincent Brault</a></li>
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<li><a href="#ot" id="toc-ot" class="nav-link" data-scroll-target="#ot"><span class="header-section-number">4.2</span> OT</a></li>
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<li><a href="#inférence-de-graphes" id="toc-inférence-de-graphes" class="nav-link" data-scroll-target="#inférence-de-graphes"><span class="header-section-number">4.3</span> Inférence de graphes</a></li>
|
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<li><a href="#causalité-1" id="toc-causalité-1" class="nav-link" data-scroll-target="#causalité-1"><span class="header-section-number">4.4</span> Causalité</a></li>
|
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<li><a href="#largest-gaps" id="toc-largest-gaps" class="nav-link" data-scroll-target="#largest-gaps"><span class="header-section-number">4.5</span> Largest Gaps</a></li>
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<section id="todo-list" class="level2" data-number="1">
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<h2 data-number="1" class="anchored" data-anchor-id="todo-list"><span class="header-section-number">1</span> TODO List</h2>
|
||
<ul>
|
||
<li><p>✅ <strong>C’est fait</strong> Passer version article flat dans Gitlab du papier et nettoyer au minimum sur une branche clean.</p></li>
|
||
<li><p>✅ Corrigée !⚠️ IL Y A UNE TYPO SUR LE SIGNE DE L’ENTROPIE POUR LE PAPIER: <span class="math inline">- \mathcal{H}</span> au lieu de <span class="math inline">+\mathcal{H}</span></p></li>
|
||
<li><p>✅ Faire tourner clustering sur Trojelsgaard. <strong>Fait mais ne sépare personne</strong>.</p></li>
|
||
<li><p>Petites opérations sur les OTUs (regarder la matrice dans les yeux):</p>
|
||
<ul>
|
||
<li>Ranger les OTUs par variances (i.e. <code>sd(OTU_j)</code>)</li>
|
||
<li>✅ <strong>Dans un RMD sur Human Microbiome Compendium</strong> Dessiner les graphiques : <span class="math inline">\mathbb{V}[OTU] = f(\mathbb{E}[OTU]), \frac{\mathbb{V}[OTU]}{\mathbb{E}[OTU]^2} = f(\mathbb{E}[OTU])</span> et <span class="math inline">\frac{\mathbb{V}[OTU]}{\mathbb{E}[OTU]} = f(\mathbb{E}[OTU]) (\approx 1)</span> si les données suivent une loi de Poisson.
|
||
<ul>
|
||
<li>HMC sur-dispersés (au-dessus bissectrice)</li>
|
||
<li>Enterotype phyloseq sous-disp</li>
|
||
</ul></li>
|
||
<li>Regarder la proportion de 1. taxon rares, 2. zeros.</li>
|
||
<li>Faire des coupures selon niveaux taxonomiques et regarder si <span class="math inline">\mathbb{V}_{\text{intra}} \approx \mathbb{V}_{\text{inter}}</span></li>
|
||
<li><em>Bonus</em>: faire ça dans qmd et voir si forge permet gitlab pages</li>
|
||
</ul></li>
|
||
<li><p>✅ Faire tourner un LBM sur Human Gut et voir si ça plante sinon, <strong>ça plante, la ram est surchargée.</strong></p>
|
||
<ul>
|
||
<li>❎⌛ Je tente avec SparseBM de JBL sur Python. <strong>Ne gère pas le Poisson</strong></li>
|
||
<li>Faire LBM sur niveau taxonomique grossier, initialiser avec le résultat pour un niveau plus fin et ainsi de suite.</li>
|
||
</ul></li>
|
||
<li><p>Increasing size : <img src="figs/tendance_temps.png" class="img-fluid"></p></li>
|
||
<li><p>⌛ Prendre jeu de données exemple de phyloseq :</p>
|
||
<ul>
|
||
<li>✅ 😞 enterotype tourne mais pas bon résultats (semble deux blocs échantillons mais pas vu par le modèle).</li>
|
||
<li>🕑 des jeux de données de Mahendra ne tourne pas (phase forward interminable).</li>
|
||
</ul></li>
|
||
<li><p>Relire <span class="citation" data-cites="peixotoHierarchicalBlockStructures2014">Peixoto (<a href="#ref-peixotoHierarchicalBlockStructures2014" role="doc-biblioref">2014</a>)</span></p>
|
||
<ul>
|
||
<li>Regarder les gens qui citent les travaux de Peixoto</li>
|
||
</ul></li>
|
||
<li><p>Implémentation <code>blockmodels</code> LBM avec covariables sur proportions (voir <a href="#eq-modele-covar-prop" class="quarto-xref">Équation 1</a>)</p></li>
|
||
</ul>
|
||
<div class="callout callout-style-default callout-note callout-titled" title="Idées">
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<div class="callout-header d-flex align-content-center">
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<i class="callout-icon"></i>
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<div class="callout-title-container flex-fill">
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Idées
|
||
</div>
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</div>
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||
<div class="callout-body-container callout-body">
|
||
<ul>
|
||
<li>Travailler sur Fungus Tree network</li>
|
||
<li>Comparaison covar prop avec GREMLINS multipartite sur (log(dist_phylo), fungus-tree)</li>
|
||
<li>Trouver manière de faire un compromis : <span class="math inline">\ell(Y,Z,W;\theta) - \lambda d(C(W),C_0)</span> avec <span class="math inline">C(W)</span> le clustering seulement sur la base de la structure LBM et <span class="math inline">C_0</span> le clustering de l’arbre. Problème <span class="math inline">d</span> est une distance entre partition, comment optimiser dessus ?</li>
|
||
<li>⌛ Mise à jour partielle des <span class="math inline">\tau</span> : ce qui pose soucis c’est les gros calculs matriciels (c’est vraiment vrai?). Donc sorte de “stochastic” VEM où on update seulement une partie des <span class="math inline">\tau</span> à chaque itération. Et échantillonnage stratifié selon l’arbre ?
|
||
<ul>
|
||
<li>⌛ Simulations avec <span class="math inline">n_2</span> croissant lancée sur Migale</li>
|
||
<li>Réimplementé VE Bernoulli dans colSBM pour Bipartite et début implémentation Stochastic VE. En fait le problème des calculs matriciels <span class="math inline">Y\times(\tau^{(1)})^{\top}</span> (<span class="math inline">n_2^2</span>) donc besoin de sous-échantillonner les noeuds de l’autre dimension à mettre à jour.</li>
|
||
</ul></li>
|
||
<li>✅ <strong>Inutile car besoin du primal</strong> Chercher à formuler le problème dual (s’il existe?) de l’optimisation du LBM. Peut-être possible d’aller plus vite alors ? <a href="#eq-dual" class="quarto-xref">Équation 2</a></li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
<ul>
|
||
<li><p>Clustering unipartite j’ai cassé une fonction de distance à vérifier et réparer</p></li>
|
||
<li><p>Codes pour le papier :</p>
|
||
<ul>
|
||
<li>Nettoyer les scripts</li>
|
||
<li>Faire un joli README</li>
|
||
<li>❓Faire des notebooks</li>
|
||
</ul></li>
|
||
<li><p>Réussir à reproduire résultat de <span class="citation" data-cites="abramovStructureKnowsBest">Abramov et al. (<a href="#ref-abramovStructureKnowsBest" role="doc-biblioref">s. d.</a>)</span></p></li>
|
||
<li><p>Maitriser graphtools de Peixoto pour essayer d’utiliser l’arbre taxonomique sur graphe de cooccurence inférer par SparCC</p></li>
|
||
<li><p>Maitriser SparCC</p></li>
|
||
<li><p>👶 (délégué à Mona) Clustering sur Doré :</p>
|
||
<ul>
|
||
<li><p>Regarder pour les couples date+nom les études et le nombre de réseaux analysables (Possible demander à Élisa)</p>
|
||
<ul>
|
||
<li>⌛ Chamberlain et al semble intéressant à regarder ! Voir le Rmarkdown</li>
|
||
</ul></li>
|
||
<li><p>Clusteriser sur la base des noms et voir parmi les réseaux Européens (désagrégés ?)</p></li>
|
||
<li><p>Si M > 10, alors voir si je retrouve les mêmes résultats que dans les études.</p></li>
|
||
<li><p>Regarder <em>Largest gap</em> sur réseaux Doré</p></li>
|
||
<li><p>⌛ Essayer <em>clustering</em> sur <code>supinfo</code></p>
|
||
<ul>
|
||
<li>CAH et Kmeans tendent vers faire <span class="math inline">K = 13</span> clusters sur les supinfos</li>
|
||
<li>Enrichir avec des métriques sur les réseaux (nestedness, connectance autres ?)</li>
|
||
<li>Demander à Elisa pour la signification des métadonnées</li>
|
||
<li>Demander à Elisa une fois vu cohérences de groupe voir pour interprétation écologiques ?</li>
|
||
<li>Algo de clustering sur les groupes trouvés</li>
|
||
</ul></li>
|
||
</ul></li>
|
||
</ul>
|
||
<section id="inférence-et-microbes" class="level3" data-number="1.1">
|
||
<h3 data-number="1.1" class="anchored" data-anchor-id="inférence-et-microbes"><span class="header-section-number">1.1</span> Inférence et microbes</h3>
|
||
<section id="modèle-avec-covariables-sur-probas-dappartenances-aux-groupes" class="level4" data-number="1.1.1">
|
||
<h4 data-number="1.1.1" class="anchored" data-anchor-id="modèle-avec-covariables-sur-probas-dappartenances-aux-groupes"><span class="header-section-number">1.1.1</span> Modèle avec covariables sur probas d’appartenances aux groupes</h4>
|
||
<p>Toujours modèle LBM mais avec probas d’appartenance pour les colonnes variables:</p>
|
||
<p><span class="math display">\begin{align*}
|
||
Z_i &\sim \mathcal{M}(1; \pi_1, \dots, \pi_Q), \sum_{q=1}^{Q} \pi_q = 1\\
|
||
W_j &\sim \mathcal{M}(1; \rho_1^j, \dots, \rho_R^j), \sum_{r=1}^{R} \rho_r^j = 1\\
|
||
Y_{i,j}&\mid Z_i = q, W_j = r \sim \mathcal{F}(\alpha_{qr})
|
||
\end{align*}</span></p>
|
||
<p>Inférence variationnelle donc <span class="math inline">\ell(Y;\pmb{\theta}) \geq \mathcal{J}(\mathcal{R},\pmb{\theta})</span> avec</p>
|
||
<p><span class="math display">
|
||
\mathcal{J}(\mathcal{R},\pmb{\theta})= \sum_{i = 1}^{n_1}\sum_{j=1}^{n_2}\sum_{q \in \mathcal{Q}_1} \sum_{r \in \mathcal{Q}_2} \tau_{iq}^{1} \tau_{jr}^{2} \log f(Y_{ij}; \alpha_{qr})
|
||
+ \sum_{i=1}^{n_1} \sum_{q \in \mathcal{Q}_1} \tau_{iq}^{1} \log \pi_{\color{black}q} + \sum_{j=1}^{n_2} \sum_{r \in \mathcal{Q}_2} \tau_{jr}^{2} \log \rho_{\color{black}r} \\
|
||
- \sum_{i=1}^{n_1} \tau_{iq}^{1} \log \tau_{iq}^{1} - \sum_{j=1}^{n_2} \tau_{jr}^{2} \log \tau_{jr}^{2}
|
||
</span></p>
|
||
<p>Plusieurs possibilités pour la définition de <span class="math inline">\rho_r^j</span></p>
|
||
<section id="modèle-sophie" class="level5" data-number="1.1.1.1">
|
||
<h5 data-number="1.1.1.1" class="anchored" data-anchor-id="modèle-sophie"><span class="header-section-number">1.1.1.1</span> Modèle Sophie</h5>
|
||
<p>Avec <span class="math inline">\rho_r^j = \frac{\exp{\beta_r X_j}}{\sum_{s=1}^{R} \exp{\beta_s X_j}} = \sigma(\pmb{\beta} \pmb{X})_{r,j}</span>, où <span class="math inline">\sigma</span> désigne le softmax. Mais il y a besoin de poser une contrainte sur l’un des <span class="math inline">(\beta_r)_{r=1,\dots,R}</span>, ici <span class="math inline">\beta_R = 0</span>.</p>
|
||
<p>La partie pertinente de l’ELBO devient: <span id="eq-modele-covar-prop"><span class="math display">
|
||
P((\beta_r)_{r=1,\dots,R}, (X_j)_{j=1,\dots,n_2}, (\tau_{jr})_{\substack{j=1,\dots,n_2\\r=1,\dots,R}} ) = \sum_{j=1}^{n_2} \sum_{r=1}^{R} [\tau_{jr} (\beta_r X_j - \log (\sum_{s=1}^{R} \exp{\beta_s X_j}))]
|
||
\tag{1}</span></span></p>
|
||
<p>Et on obtient la dérivée partielle par rapport à <span class="math inline">\beta_t</span> comme: <span class="math display">\begin{align*}
|
||
\dfrac{\partial P}{\partial \beta_t}&((\beta_r)_{r=1,\dots,R}, (X_j)_{j=1,\dots,n_2}, (\tau_{jr})_{\substack{j=1,\dots,n_2\\r=1,\dots,R}} ) = \sum_{j=1}^{n_2} \biggl[ \tau_{jt} X_j - \frac{X_j \exp{\beta_t X_j}}{\sum_{s=1}^{R} \exp{\beta_s X_j}} \biggr]\\
|
||
& = \sum_{j=1}^{n_2} \biggl[\bigl(\tau_{jt} - \sigma(\pmb{\beta} \pmb{X})_{t,j}\bigr) X_j\biggr] = \sum_{j=1}^{n_2} \biggl[\bigl(\tau_{jt} - \rho_t^j \bigr) X_j\biggr]
|
||
\end{align*}</span></p>
|
||
</section>
|
||
</section>
|
||
<section id="idée-du-problème-dual" class="level4" data-number="1.1.2">
|
||
<h4 data-number="1.1.2" class="anchored" data-anchor-id="idée-du-problème-dual"><span class="header-section-number">1.1.2</span> Idée du problème dual</h4>
|
||
<p>Les distributions variationnelles sont définies par :</p>
|
||
<p><span class="math display">
|
||
q(Z,W)
|
||
=
|
||
\prod_{i=1}^{n_1} q_i(Z_i)
|
||
\prod_{j=1}^{n_2} q_j(W_j),
|
||
</span></p>
|
||
<p>avec <span class="math display">
|
||
q_i(Z_i=q)=\tau_{iq}^{(1)},
|
||
\qquad
|
||
q_j(W_j=r)=\tau_{jr}^{(2)}.
|
||
</span></p>
|
||
<p>Les contraintes de normalisation sont : <span class="math display">
|
||
\sum_{q=1}^Q \tau_{iq}^{(1)} = 1,
|
||
\qquad
|
||
\sum_{r=1}^R \tau_{jr}^{(2)} = 1.
|
||
</span></p>
|
||
<hr>
|
||
<section id="lagrangien" class="level5" data-number="1.1.2.1">
|
||
<h5 data-number="1.1.2.1" class="anchored" data-anchor-id="lagrangien"><span class="header-section-number">1.1.2.1</span> Lagrangien</h5>
|
||
<p>Le lagrangien du problème variationnel s’écrit : <span class="math display">
|
||
\mathcal{L}\!\left(
|
||
\tau^{(1)},\tau^{(2)},(\lambda_i)_{i=1}^{n_1},(\mu_j)_{j=1}^{n_2}
|
||
\right)
|
||
=
|
||
\mathcal{J}(\mathcal{R},\pmb{\theta})
|
||
+
|
||
\sum_{i=1}^{n_1} \lambda_i
|
||
\left(1-\sum_{q=1}^Q \tau_{iq}^{(1)}\right)
|
||
+
|
||
\sum_{j=1}^{n_2} \mu_j
|
||
\left(1-\sum_{r=1}^R \tau_{jr}^{(2)}\right),
|
||
</span> où <span class="math inline">\mathcal{J}(\mathcal{R},\pmb{\theta})</span> désigne la borne inférieure variationnelle associée au modèle et aux paramètres <span class="math inline">\Theta</span>.</p>
|
||
<hr>
|
||
</section>
|
||
<section id="problème-primal-conditions-doptimalité" class="level5" data-number="1.1.2.2">
|
||
<h5 data-number="1.1.2.2" class="anchored" data-anchor-id="problème-primal-conditions-doptimalité"><span class="header-section-number">1.1.2.2</span> Problème primal (conditions d’optimalité)</h5>
|
||
<p>En dérivant le lagrangien par rapport aux variables variationnelles <span class="math inline">\tau^{(1)}</span> et <span class="math inline">\tau^{(2)}</span>, puis en égalisant à zéro, on obtient les équations de point fixe suivantes :</p>
|
||
<p><span class="math display">
|
||
\tau_{iq}^{(1)}
|
||
\propto
|
||
\pi_q^{(t)}
|
||
\prod_{j=1}^{n_2}
|
||
\prod_{r=1}^{R}
|
||
f\!\left(Y_{ij};\alpha_{qr}^{(t)}\right)^{\tau_{jr}^{(2),(t+1)}},
|
||
\quad
|
||
\forall i=1,\dots,n_1,\;
|
||
q=1,\dots,Q,
|
||
</span></p>
|
||
<p><span class="math display">
|
||
\tau_{jr}^{(2)}
|
||
\propto
|
||
\rho_r^{(t)}
|
||
\prod_{i=1}^{n_1}
|
||
\prod_{q=1}^{Q}
|
||
f\!\left(Y_{ij};\alpha_{qr}^{(t)}\right)^{\tau_{iq}^{(1),(t+1)}},
|
||
\quad
|
||
\forall j=1,\dots,n_2,\;
|
||
r=1,\dots,R,
|
||
</span> où :</p>
|
||
<ul>
|
||
<li><span class="math inline">\pi_q^{(t)}</span> et <span class="math inline">\rho_r^{(t)}</span> sont les proportions de classes,</li>
|
||
<li><span class="math inline">f(\cdot;\alpha_{qr})</span> est la loi d’émission du modèle,</li>
|
||
<li><span class="math inline">\alpha_{qr}^{(t)}</span> désigne les paramètres de bloc à l’itération <span class="math inline">t</span>.</li>
|
||
</ul>
|
||
<hr>
|
||
</section>
|
||
<section id="constantes-de-normalisation" class="level5" data-number="1.1.2.3">
|
||
<h5 data-number="1.1.2.3" class="anchored" data-anchor-id="constantes-de-normalisation"><span class="header-section-number">1.1.2.3</span> Constantes de normalisation</h5>
|
||
<p>Les constantes de normalisation associées sont données par :</p>
|
||
<p><span class="math display">
|
||
T^{(1),(t)}_i
|
||
=
|
||
\sum_{q=1}^{Q}
|
||
\pi_q^{(t)}
|
||
\exp\!\left(
|
||
\sum_{j=1}^{n_2}
|
||
\sum_{r=1}^{R}
|
||
\tau_{jr}^{(2)}
|
||
\log f\!\left(Y_{ij};\alpha_{qr}^{(t)}\right)
|
||
\right),
|
||
</span></p>
|
||
<p><span class="math display">
|
||
T^{(2),(t)}_j
|
||
=
|
||
\sum_{r=1}^{R}
|
||
\rho_r^{(t)}
|
||
\exp\!\left(
|
||
\sum_{i=1}^{n_1}
|
||
\sum_{q=1}^{Q}
|
||
\tau_{iq}^{(1)}
|
||
\log f\!\left(Y_{ij};\alpha_{qr}^{(t)}\right)
|
||
\right).
|
||
</span></p>
|
||
<p>Ainsi, les mises à jour normalisées s’écrivent : <span class="math display">
|
||
\tau_{iq}^{(1)} = \frac{1}{T^{(1),(t)}_i}(\cdots),
|
||
\qquad
|
||
\tau_{jr}^{(2)} = \frac{1}{T^{(2),(t)}_j}(\cdots).
|
||
</span></p>
|
||
<hr>
|
||
</section>
|
||
<section id="interprétation-duale" class="level5" data-number="1.1.2.4">
|
||
<h5 data-number="1.1.2.4" class="anchored" data-anchor-id="interprétation-duale"><span class="header-section-number">1.1.2.4</span> Interprétation duale</h5>
|
||
<p>Les multiplicateurs de Lagrange s’identifient alors à : <span id="eq-dual"><span class="math display">
|
||
\lambda_i = -\log T^{(1),(t)}_i - 1,
|
||
\qquad
|
||
\mu_j = -\log T^{(2),(t)}_j - 1,
|
||
\tag{2}</span></span> et le problème dual consiste à minimiser une somme de fonctions de log-partition, ce qui montre que l’algorithme VEM réalise implicitement une descente sur le dual.</p>
|
||
</section>
|
||
</section>
|
||
<section id="bibliographie-à-lire-à-faire" class="level4" data-number="1.1.3">
|
||
<h4 data-number="1.1.3" class="anchored" data-anchor-id="bibliographie-à-lire-à-faire"><span class="header-section-number">1.1.3</span> Bibliographie: à lire, à faire</h4>
|
||
<ul>
|
||
<li>Lire article multi-niveaux Saint-Clair</li>
|
||
<li>🆕 🔎 Trouver des papiers:
|
||
<ul>
|
||
<li>LBM Negative Binomial</li>
|
||
<li>Network inference through sample comparison</li>
|
||
</ul></li>
|
||
<li>Idée des groupes sur la base de distance phylogénétique:
|
||
<ul>
|
||
<li>En train de comprendre les distances que phyloseq permet de calculer sur notre exemple</li>
|
||
<li>En train de lire sur Principle coordinate analysis : https://openplantpathology.github.io/OPP_Workshop_Multivariate/2-MV_PCO.html</li>
|
||
<li>Parametric t-SNE pour avoir une unique représentation latente (inconvénient utilise du Deep Learning)</li>
|
||
<li>Lire Papier UniFrac</li>
|
||
</ul></li>
|
||
</ul>
|
||
</section>
|
||
<section id="réflexion" class="level4" data-number="1.1.4">
|
||
<h4 data-number="1.1.4" class="anchored" data-anchor-id="réflexion"><span class="header-section-number">1.1.4</span> Réflexion</h4>
|
||
<ul>
|
||
<li>easy16s : se renseigner sur
|
||
<ul>
|
||
<li><span class="math inline">\alpha</span>, <span class="math inline">\beta</span> diversité</li>
|
||
<li>Heatmap</li>
|
||
</ul></li>
|
||
<li>Regarder <strong>SPARTA</strong> Rennes</li>
|
||
<li>Ecrire et étudier les modèles pour différents niveaux taxonomiques.</li>
|
||
<li>🆕 Regarder NetComi</li>
|
||
<li>🆕 Regarder OneNet car aggrégation plus robuste</li>
|
||
<li>🆕 Réfléchir sens d’aggréger les données ou de les diviser</li>
|
||
</ul>
|
||
</section>
|
||
<section id="écrire-et-faire-tourner" class="level4" data-number="1.1.5">
|
||
<h4 data-number="1.1.5" class="anchored" data-anchor-id="écrire-et-faire-tourner"><span class="header-section-number">1.1.5</span> Écrire et faire tourner</h4>
|
||
<ul>
|
||
<li>Lancer <em>colBiSBM</em> sur <span class="math inline">OTU\times Sample</span> → problème du chargement en mémoire des données à voir</li>
|
||
<li>Lancer <em>colSBM</em> sur <span class="math inline">OTU\times OTU</span></li>
|
||
<li>TabNet pratiquer les <a href="https://github.com/cregouby/Tutoriel_torch">exercices</a></li>
|
||
<li>🆕 SparCC à différent niveaux</li>
|
||
<li>🆕 SBM à différent niveaux</li>
|
||
<li>🆕⌛ Tree-PLN à différents niveaux</li>
|
||
</ul>
|
||
</section>
|
||
<section id="causalité" class="level4" data-number="1.1.6">
|
||
<h4 data-number="1.1.6" class="anchored" data-anchor-id="causalité"><span class="header-section-number">1.1.6</span> Causalité</h4>
|
||
<p>Plus sur le temps long, à regarder</p>
|
||
<ul>
|
||
<li>GT causalité</li>
|
||
<li>Daria Bystrova lire présentation <span class="citation" data-cites="bystrovaCausalDiscovery">Bystrova (<a href="#ref-bystrovaCausalDiscovery" role="doc-biblioref">s. d.</a>)</span> (Meek rules, V-structure)</li>
|
||
</ul>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="a-discuter" class="level2" data-number="2">
|
||
<h2 data-number="2" class="anchored" data-anchor-id="a-discuter"><span class="header-section-number">2</span> A discuter</h2>
|
||
<ul>
|
||
<li>🆕 Voir pour des Réseaux / GDR ou aller</li>
|
||
<li>🆕 Chercher des cours à suivre</li>
|
||
</ul>
|
||
</section>
|
||
<section id="biblio-à-faire" class="level2" data-number="3">
|
||
<h2 data-number="3" class="anchored" data-anchor-id="biblio-à-faire"><span class="header-section-number">3</span> Biblio à faire</h2>
|
||
<ul>
|
||
<li>Regarder Transport optimal graphes bipartite.</li>
|
||
</ul>
|
||
</section>
|
||
<section id="lectures-en-cours" class="level2" data-number="4">
|
||
<h2 data-number="4" class="anchored" data-anchor-id="lectures-en-cours"><span class="header-section-number">4</span> Lectures en cours 📚</h2>
|
||
<section id="hdr-vincent-brault" class="level3" data-number="4.1">
|
||
<h3 data-number="4.1" class="anchored" data-anchor-id="hdr-vincent-brault"><span class="header-section-number">4.1</span> HDR Vincent Brault</h3>
|
||
<ul>
|
||
<li>⌛ Chap 2 : Creuser l’idée de maximiser l’énergie libre, très intéressant regarder le critère CARI et lire Robert et al 2021. Actuellement p32 du manuscrit</li>
|
||
<li>Chap 3</li>
|
||
</ul>
|
||
</section>
|
||
<section id="ot" class="level3" data-number="4.2">
|
||
<h3 data-number="4.2" class="anchored" data-anchor-id="ot"><span class="header-section-number">4.2</span> OT</h3>
|
||
<ul>
|
||
<li>⌛ <span class="citation" data-cites="mazeletUnsupervisedLearningOptimal">Mazelet, Flamary, et Thirion (<a href="#ref-mazeletUnsupervisedLearningOptimal" role="doc-biblioref">s. d.</a>)</span> Intéressant pour le transport optimal entre graphes de tailles différentes | Regarder si regularization entropique ne marche pas bien pour le graphe.</li>
|
||
<li>⌛ <span class="citation" data-cites="nennaLecture2Entropic">Nenna (<a href="#ref-nennaLecture2Entropic" role="doc-biblioref">s. d.b</a>)</span> Pour comprendre le problème d’OT régularisé pour l’entropie.</li>
|
||
<li>⌛ <span class="citation" data-cites="nennaLecture1Monge">Nenna (<a href="#ref-nennaLecture1Monge" role="doc-biblioref">s. d.a</a>)</span></li>
|
||
</ul>
|
||
</section>
|
||
<section id="inférence-de-graphes" class="level3" data-number="4.3">
|
||
<h3 data-number="4.3" class="anchored" data-anchor-id="inférence-de-graphes"><span class="header-section-number">4.3</span> Inférence de graphes</h3>
|
||
<ul>
|
||
<li><p>⌛ <span class="citation" data-cites="aitchisonStatisticalAnalysisCompositional1982a">Aitchison (<a href="#ref-aitchisonStatisticalAnalysisCompositional1982a" role="doc-biblioref">1982</a>)</span>, en cours</p></li>
|
||
<li><p>❗📖 <span class="citation" data-cites="payneFiniteMixturesMultivariate2023">Payne et al. (<a href="#ref-payneFiniteMixturesMultivariate2023" role="doc-biblioref">2023</a>)</span> sur MixMPLN</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="causalité-1" class="level3" data-number="4.4">
|
||
<h3 data-number="4.4" class="anchored" data-anchor-id="causalité-1"><span class="header-section-number">4.4</span> Causalité</h3>
|
||
<ul>
|
||
<li>❗📖 <span class="citation" data-cites="bystrovaCausalDiscovery">Bystrova (<a href="#ref-bystrovaCausalDiscovery" role="doc-biblioref">s. d.</a>)</span></li>
|
||
</ul>
|
||
</section>
|
||
<section id="largest-gaps" class="level3" data-number="4.5">
|
||
<h3 data-number="4.5" class="anchored" data-anchor-id="largest-gaps"><span class="header-section-number">4.5</span> Largest Gaps</h3>
|
||
<ul>
|
||
<li>❗📖 <span class="citation" data-cites="braultFastConsistentAlgorithm2023">Brault et Channarond (<a href="#ref-braultFastConsistentAlgorithm2023" role="doc-biblioref">2023</a>)</span></li>
|
||
<li>❗📖 <span class="citation" data-cites="channarondClassificationEstimationStochastic2012">Channarond, Daudin, et Robin (<a href="#ref-channarondClassificationEstimationStochastic2012" role="doc-biblioref">2012</a>)</span> le papier qui introduit le <em>Largest Gaps</em></li>
|
||
</ul>
|
||
|
||
|
||
|
||
</section>
|
||
</section>
|
||
|
||
<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography" id="quarto-bibliography"><h2 class="anchored quarto-appendix-heading">Les références</h2><div id="refs" class="references csl-bib-body hanging-indent" data-entry-spacing="0" role="list">
|
||
<div id="ref-abramovStructureKnowsBest" class="csl-entry" role="listitem">
|
||
Abramov, Kesem, Barry Biton, Geut Galai, Rami Puzis, et Shai Pilosof. s. d. <span>« Structure Knows Best: Predicting Ecological Interactions Across Space Through Pairwise Integration of Latent Network Patterns »</span>.
|
||
</div>
|
||
<div id="ref-aitchisonStatisticalAnalysisCompositional1982a" class="csl-entry" role="listitem">
|
||
Aitchison, J. 1982. <span>« The <span>Statistical Analysis</span> of <span>Compositional Data</span> »</span>. <em>Journal of the Royal Statistical Society. Series B (Methodological)</em> 44 (2): 139‑77. <a href="https://www.jstor.org/stable/2345821">https://www.jstor.org/stable/2345821</a>.
|
||
</div>
|
||
<div id="ref-braultFastConsistentAlgorithm2023" class="csl-entry" role="listitem">
|
||
Brault, Vincent, et Antoine Channarond. 2023. <span>« Fast and <span>Consistent Algorithm</span> for the <span>Latent Block Model</span> »</span>. 9 mars 2023. <a href="https://doi.org/10.48550/arXiv.1610.09005">https://doi.org/10.48550/arXiv.1610.09005</a>.
|
||
</div>
|
||
<div id="ref-bystrovaCausalDiscovery" class="csl-entry" role="listitem">
|
||
Bystrova, Daria. s. d. <span>« Causal Discovery »</span>.
|
||
</div>
|
||
<div id="ref-channarondClassificationEstimationStochastic2012" class="csl-entry" role="listitem">
|
||
Channarond, Antoine, Jean-Jacques Daudin, et Stéphane Robin. 2012. <span>« Classification and Estimation in the <span>Stochastic Blockmodel</span> Based on the Empirical Degrees »</span>. <em>Electronic Journal of Statistics</em> 6 (janvier). <a href="https://doi.org/10.1214/12-ejs753">https://doi.org/10.1214/12-ejs753</a>.
|
||
</div>
|
||
<div id="ref-mazeletUnsupervisedLearningOptimal" class="csl-entry" role="listitem">
|
||
Mazelet, Sonia, Rémi Flamary, et Bertrand Thirion. s. d. <span>« Unsupervised <span>Learning</span> for <span>Optimal Transport</span> Plan Prediction Between Unbalanced Graphs »</span>.
|
||
</div>
|
||
<div id="ref-nennaLecture1Monge" class="csl-entry" role="listitem">
|
||
Nenna, Luca. s. d.a. <span>« Lecture 1 <span>Monge</span> and <span>Kantorovich</span> Problems: From Primal to Dual »</span>.
|
||
</div>
|
||
<div id="ref-nennaLecture2Entropic" class="csl-entry" role="listitem">
|
||
———. s. d.b. <span>« Lecture 2: <span>Entropic Optimal Transport</span> »</span>.
|
||
</div>
|
||
<div id="ref-payneFiniteMixturesMultivariate2023" class="csl-entry" role="listitem">
|
||
Payne, Andrea, Anjali Silva, Steven J. Rothstein, Paul D. McNicholas, et Sanjeena Subedi. 2023. <span>« Finite <span>Mixtures</span> of <span>Multivariate Poisson-Log Normal Factor Analyzers</span> for <span>Clustering Count Data</span> »</span>. 13 novembre 2023. <a href="https://doi.org/10.48550/arXiv.2311.07762">https://doi.org/10.48550/arXiv.2311.07762</a>.
|
||
</div>
|
||
<div id="ref-peixotoHierarchicalBlockStructures2014" class="csl-entry" role="listitem">
|
||
Peixoto, Tiago P. 2014. <span>« Hierarchical <span>Block Structures</span> and <span>High-Resolution Model Selection</span> in <span>Large Networks</span> »</span>. <em>Physical Review X</em> 4 (1): 011047. <a href="https://doi.org/10.1103/PhysRevX.4.011047">https://doi.org/10.1103/PhysRevX.4.011047</a>.
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el,
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const ref = bibliorefs[i];
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tippyHover(citeInfo.el, function() {
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citeInfo.cites.forEach(function(cite) {
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citeDiv.classList.add('hanging-indent');
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citeDiv.classList.add('csl-entry');
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var biblioDiv = window.document.getElementById('ref-' + cite);
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citeDiv.innerHTML = biblioDiv.innerHTML;
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</div> <!-- /content -->
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</body></html> |