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61b5f3ccbd
...
9a564750e2
3 changed files with 236 additions and 158 deletions
101
.obsidian/workspace.json
vendored
101
.obsidian/workspace.json
vendored
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@ -6,20 +6,63 @@
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"title": "SBM avec covariance latente"
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@ -197,19 +240,9 @@
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@ -235,43 +268,43 @@
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"Thèse/Axes/Phylogénie/SBM avec covariance multinomiale probit.md",
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"Thèse/Axes/Phylogénie/SBM avec covariance latente.md",
|
||||
"Résumé des tâches.md",
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"Thèse/StateOfTheR/HappyR/2026-05-29 MLOps en Python.md",
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||||
"Thèse/Résolution des problèmes/Problème avec renv.md",
|
||||
"Thèse/Packages/R/colSBM.md",
|
||||
"Thèse/Projets annexes/VGAE avec (Gromov-)Wasserstein.md",
|
||||
"Thèse/Projets annexes/Applications colBiSBM pour impact pratiques agris sur interactions plantes pollinisateurs.md",
|
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"Thèse/Projets annexes/Application colBiSBM réseaux d'optimisation de NN.md",
|
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"Thèse/Projets annexes",
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"Thèse/Articles/Review papier colBiSBM.md",
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"Thèse/Packages/R",
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"Thèse/Packages",
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"public/index-listing.json",
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"public/Thèse/Utile/Doranum.html",
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"public/Thèse/Utile",
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"public/Thèse/TODO/2026-05-18.html",
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"public/Thèse/TODO",
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"public/Thèse/Séminaires/2026-06-09 FRANCHETERRE Blanche.html",
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"public/Thèse/Séminaires/2026-05-21 CHENNETIER Guillaume.html",
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"Thèse/Projets annexes/Application colBiSBM réseaux d'optimisation de NN.md",
|
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"Thèse/Projets annexes/Applications colBiSBM pour impact pratiques agris sur interactions plantes pollinisateurs.md",
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"Thèse/TODO/2026-05-18.md",
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"macros.tex.md",
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"Thèse/Lectures/local_macros.tex.md",
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"Thèse/Projets annexes/VGAE avec (Gromov-)Wasserstein.md",
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"Thèse/Projets annexes",
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"Thèse/Axes/Phylogénie/SBM avec covariance latente.md",
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"Thèse/Lectures/@quericBridgingMaximumLikelihood2026.md",
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"@quericBridgingMaximumLikelihood2026.md",
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"Thèse/Articles/Review papier colBiSBM.md",
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"Thèse/TODO/2026-05-18.md",
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"Thèse/Résumés séminaires.md",
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"Thèse/Séminaires/2026-06-09 VICTOR François.md",
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"Thèse/Séminaires/2026-06-09 FRANCHETERRE Blanche.md",
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||||
"Perso/Tâches/2026-05-17.md",
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"Thèse/Axes/projets-phylo.qmd",
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"Thèse/Tutoriel ABC.md",
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"Bienvenue.md",
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"Thèse/Lectures/@turnerTutorialApproximateBayesian2012.md",
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"Thèse/Lectures/@hronImputationMissingValues2010.md",
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"Thèse/Axes/Phylogénie/SBM avec covariance multinomiale probit.md",
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"Thèse/Axes/Phylogénie/Phylogénie Papiers à regarder.md",
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"Perso/Tâches/Casque antibruit pour l'anniversaire de Kris.md",
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"Thèse/StateOfTheR/HappyR/2026-05-29 MLOps en Python.md",
|
||||
"@boraCompressedSensingUsing2017.md",
|
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"Thèse/Groupes de travail/Modèles génératifs/VAE pour la régularisation de problème inverse.md",
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"Thèse/Séminaires/2026-05-28 SILVA BERNARDES Juliana.md",
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"Meta/Modèles/Séminaire_Template.md"
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"Thèse/StateOfTheR/HappyR/Sans titre",
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"Thèse/StateOfTheR/HappyR",
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"Thèse/StateOfTheR",
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"Thèse/Groupes de travail/Modèles génératifs",
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"Thèse/Groupes de travail",
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"public/index-listing.json"
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]
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}
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@ -1,6 +1,4 @@
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# Inclusion dans la thèse
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Ce modèle ci est une proposition pour remettre en cause l'hypothèse du LBM d'indépendance des $Z_{i}$ en définissant une structure de dépendance dépendantes de la phylogénie.
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# Idée du modèle
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@ -35,191 +33,238 @@ avec $\Sigma$, la matrice de variance-covariance déterminée en fonction de l'a
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\usepackage{amsmath,amssymb}
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||||
\usetikzlibrary{
|
||||
\usetikzlibrary{arrows.meta,positioning,shapes.geometric,calc}
|
||||
|
||||
arrows.meta,
|
||||
\begin{document}
|
||||
\begin{tikzpicture}[
|
||||
font=\sffamily,
|
||||
>=Latex,
|
||||
node distance=1.5cm and 2cm,
|
||||
directed/.style={-{Latex}, line width=0.8pt, draw=gray!75},
|
||||
bidirected/.style={-, line width=0.8pt, draw=red!75},
|
||||
base/.style={
|
||||
draw=gray!70,
|
||||
line width=0.9pt,
|
||||
align=center,
|
||||
inner sep=4pt
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||||
},
|
||||
prior/.style={base,rectangle,rounded corners=1pt,fill=blue!7},
|
||||
latent/.style={base,rectangle,rounded corners=6pt,fill=teal!8},
|
||||
known/.style={base,diamond,aspect=1.35,fill=orange!12},
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||||
observed/.style={base,circle,fill=purple!8}
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||||
]
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||||
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positioning,
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%--------------------------------------------------
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||||
% Hyperparameters rows
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||||
%--------------------------------------------------
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||||
\node[prior] (sigma) {$\sigma^2$};
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||||
\node[known,right=of sigma] (Sigma) {$\Sigma$};
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||||
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shapes.geometric,
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\node[latent,below=of sigma] (Pi) {$P_i$};
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||||
\node[latent,below=of Sigma] (Pip) {$P_{i'}$};
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||||
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calc,
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\node[latent,below=of Pi] (Zi) {$Z_i$};
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\node[latent,below=of Pip] (Zip) {$Z_{i'}$};
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fit
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||||
%--------------------------------------------------
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||||
% Hyperparameters columns
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||||
%--------------------------------------------------
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||||
\node[prior,right=4cm of Sigma] (rho) {$\rho$};
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||||
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}
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\node[latent,below left=of rho] (Wj) {$W_j$};
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||||
\node[latent,below right=of rho] (Wjp) {$W_{j'}$};
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||||
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||||
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||||
%--------------------------------------------------
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||||
% Intercept
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||||
%--------------------------------------------------
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||||
\node[prior] (alpha)
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||||
at ($(Zi)!0.5!(Wj)+(0,-3)$)
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||||
{$\alpha$};
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||||
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||||
%--------------------------------------------------
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||||
% Observations
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||||
%--------------------------------------------------
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||||
\node[observed]
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||||
at ($(Zi)!0.5!(Wj)+(0,-1.4)$)
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||||
(Yij) {$Y_{ij}$};
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||||
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||||
\node[observed]
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||||
at ($(Zi)!0.5!(Wjp)+(2.0,-1.4)$)
|
||||
(Yijp) {$Y_{ij'}$};
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||||
|
||||
\node[observed]
|
||||
at ($(Zip)!0.5!(Wj)+(-2.0,-1.4)$)
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||||
(Yipj) {$Y_{i'j}$};
|
||||
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||||
\node[observed]
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||||
at ($(Zip)!0.5!(Wjp)+(0,-1.4)$)
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||||
(Yipjp) {$Y_{i'j'}$};
|
||||
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||||
%--------------------------------------------------
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||||
% Row side
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||||
%--------------------------------------------------
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||||
\draw[directed] (sigma) -- (Pi);
|
||||
\draw[directed] (Sigma) -- (Pi);
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||||
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||||
\draw[directed] (sigma) -- (Pip);
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||||
\draw[directed] (Sigma) -- (Pip);
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||||
|
||||
\draw[directed] (Pi) -- (Zi);
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||||
\draw[directed] (Pip) -- (Zip);
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||||
|
||||
%--------------------------------------------------
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||||
% Column side
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||||
%--------------------------------------------------
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||||
\draw[directed] (rho) -- (Wj);
|
||||
\draw[directed] (rho) -- (Wjp);
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||||
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||||
%--------------------------------------------------
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||||
% Likelihood
|
||||
%--------------------------------------------------
|
||||
\foreach \y in {Yij,Yijp}
|
||||
\draw[directed] (Zi) -- (\y);
|
||||
|
||||
\foreach \y in {Yipj,Yipjp}
|
||||
\draw[directed] (Zip) -- (\y);
|
||||
|
||||
\foreach \y in {Yij,Yipj}
|
||||
\draw[directed] (Wj) -- (\y);
|
||||
|
||||
\foreach \y in {Yijp,Yipjp}
|
||||
\draw[directed] (Wjp) -- (\y);
|
||||
|
||||
\foreach \y in {Yij,Yijp,Yipj,Yipjp}
|
||||
\draw[directed] (alpha) -- (\y);
|
||||
|
||||
%--------------------------------------------------
|
||||
% Correlation structure
|
||||
%--------------------------------------------------
|
||||
\draw[bidirected] (alpha) -- (Zi);
|
||||
\draw[bidirected] (alpha) -- (Zip);
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||||
|
||||
\draw[bidirected] (alpha) -- (Wj);
|
||||
\draw[bidirected] (alpha) -- (Wjp);
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
```
|
||||
|
||||
```tikz
|
||||
\usepackage{tikz}
|
||||
|
||||
\usepackage{amsmath}
|
||||
|
||||
\usetikzlibrary{positioning,shapes.arrows, arrows.meta,shapes.geometric}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{tikzpicture}[
|
||||
\begin{tikzpicture}
|
||||
|
||||
font=\sffamily,
|
||||
\tikzset{
|
||||
|
||||
>=Latex,
|
||||
every path/.append style = {
|
||||
|
||||
node distance=1cm and 0.25cm,
|
||||
arrows = ->,
|
||||
|
||||
directed/.style={-{Latex}, line width=0.8pt, draw=gray!75},
|
||||
> = stealth,},
|
||||
|
||||
bidirected/.style={-, line width=0.8pt, draw=red!75},
|
||||
every node/.append style = {
|
||||
|
||||
base/.style={
|
||||
shape = circle,
|
||||
|
||||
draw=gray!70,
|
||||
draw = black,
|
||||
|
||||
line width=0.9pt,
|
||||
|
||||
align=center,
|
||||
|
||||
inner sep=4pt
|
||||
minimum size=3em
|
||||
|
||||
},
|
||||
|
||||
prior/.style={base,rectangle,rounded corners=1pt,fill=blue!7},
|
||||
latent/.style = {
|
||||
|
||||
latent/.style={base,rectangle,rounded corners=6pt,fill=teal!8},
|
||||
fill = lightgray
|
||||
|
||||
known/.style={base,diamond,aspect=1.35,fill=orange!12},
|
||||
},
|
||||
|
||||
observed/.style={base,circle,fill=purple!8},
|
||||
prior/.style = {
|
||||
|
||||
plate/.style={
|
||||
fill = red},
|
||||
|
||||
draw=black!60,
|
||||
moral/.style = {
|
||||
|
||||
rounded corners,
|
||||
dashed,
|
||||
|
||||
inner sep=8pt
|
||||
> = {}, % remove arrow tip
|
||||
|
||||
}
|
||||
arrows = -, % ensure no arrows
|
||||
|
||||
]
|
||||
}}
|
||||
|
||||
|
||||
|
||||
%--------------------------------------------------
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||||
|
||||
% Row clustering
|
||||
|
||||
%--------------------------------------------------
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||||
\node (y) {$Y$};
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||||
|
||||
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||||
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||||
\node[prior] (sigma) {$\sigma^2$};
|
||||
|
||||
\node[known,right=of sigma] (Sigma) {$\Sigma$};
|
||||
\node[latent] (z) [above left = of y] {$Z$};
|
||||
|
||||
|
||||
|
||||
\node[latent,below=of sigma] (Pi) {$P_i$};
|
||||
|
||||
\node[latent,below=0.5cm of Pi] (Zi) {$Z_i$};
|
||||
\node[latent] (w) [above right = of y] {$W$};
|
||||
|
||||
|
||||
|
||||
\draw[directed] (sigma) -- (Pi);
|
||||
|
||||
\draw[directed] (Sigma) -- (Pi);
|
||||
|
||||
\draw[directed] (Pi) -- (Zi);
|
||||
\node[latent] (P) [above = of z] {$P$};
|
||||
|
||||
|
||||
|
||||
%--------------------------------------------------
|
||||
|
||||
% Column clustering
|
||||
|
||||
%--------------------------------------------------
|
||||
|
||||
\node[latent,right=2.5cm of Zi] (Wj) {$W_j$};
|
||||
\node[prior] (sigma2) [above = of P] {$\sigma^2$};
|
||||
|
||||
|
||||
|
||||
\node[prior] (rho) at (Wj |- sigma) {$\rho$};
|
||||
\node[prior] (rho) [above = of w] {$\rho_{1:R}$};
|
||||
|
||||
|
||||
|
||||
\draw[directed] (rho) -- (Wj);
|
||||
\node[prior] (alpha) [below = of y] {$\boldsymbol{\alpha}$};
|
||||
|
||||
|
||||
|
||||
%--------------------------------------------------
|
||||
|
||||
% Observation
|
||||
|
||||
%--------------------------------------------------
|
||||
\path (z) edge (y);
|
||||
|
||||
|
||||
|
||||
\node[observed] (Yij)
|
||||
|
||||
at ($(Zi)!0.5!(Wj)+(0,-0.9)$)
|
||||
|
||||
{$Y_{ij}$};
|
||||
\path (w) edge (y);
|
||||
|
||||
|
||||
|
||||
\draw[directed] (Zi) -- (Yij);
|
||||
|
||||
\draw[directed] (Wj) -- (Yij);
|
||||
\path (rho) edge (w);
|
||||
|
||||
|
||||
|
||||
\draw[bidirected] (Zi) -- (Wj);
|
||||
\path (alpha) edge (y);
|
||||
|
||||
|
||||
|
||||
%--------------------------------------------------
|
||||
|
||||
% Intercept
|
||||
|
||||
%--------------------------------------------------
|
||||
\path (P) edge (z);
|
||||
|
||||
|
||||
|
||||
\node[prior] (alpha)
|
||||
|
||||
at ($(Yij)+(0,-2.5)$)
|
||||
|
||||
{$\alpha$};
|
||||
\path (sigma2) edge (P);
|
||||
|
||||
|
||||
|
||||
\draw[directed] (alpha) -- (Yij);
|
||||
% moral
|
||||
|
||||
|
||||
|
||||
\draw[bidirected] (alpha) -- (Zi);
|
||||
|
||||
\draw[bidirected] (alpha) -- (Wj);
|
||||
\path[moral] (z) edge (alpha);
|
||||
|
||||
|
||||
|
||||
%--------------------------------------------------
|
||||
|
||||
% Plates
|
||||
|
||||
%--------------------------------------------------
|
||||
\path[moral] (w) edge (alpha);
|
||||
|
||||
|
||||
|
||||
\node[plate,fit=(Pi)(Zi),label={[align=center]left:$i=1,\ldots,n_1$}] {};
|
||||
|
||||
|
||||
|
||||
\node[plate,fit=(Wj),label={[align=center]right:$j=1,\ldots,n_2$}] {};
|
||||
|
||||
|
||||
|
||||
\node[plate,
|
||||
|
||||
fit=(Yij),
|
||||
|
||||
label=below right:{$(i,j)$}] {};
|
||||
|
||||
|
||||
\path[moral] (z) edge (w);
|
||||
|
||||
\end{tikzpicture}
|
||||
|
||||
|
|
@ -600,14 +645,14 @@ $$
|
|||
\end{align*}
|
||||
$$
|
||||
|
||||
En posant $R_{ir}^W=\sum_{j=1}^{n_{2}}W_{jr}Y_{ij}$ et $F_{ir}^W =\sum_{j=1}^{n_{2}}W_{jr}(1-Y_{ij})$ on définit les matrices $\mathbf{R}^W$ et $\mathbf{F}^W$ qui comptent les succès et échecs par ligne $i$ et groupe $r$.
|
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En posant $R_{ir}=\sum_{j=1}^{n_{2}}W_{jr}Y_{ij}$ et $F_{ir}=\sum_{j=1}^{n_{2}}W_{jr}(1-Y_{ij})$ on définit les matrices $\mathbf{R}$ et $\mathbf{F}$ qui comptent les succès et échecs par ligne $i$ et groupe $r$.
|
||||
|
||||
Ce qui donne pour les $\tilde{\pi}_{i,k}$ de la posterior:
|
||||
|
||||
$$
|
||||
\begin{align*}
|
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\tilde{\pi}_{i,k} = p(Z_{i} = k\mid Y_{i,\bullet},\alpha,W,P_{i}) & \propto p(Y_{i,\bullet}\mid Z_{i} = k, \alpha, W, P_{i})p(Z_{i}=k\mid P_{i})\\
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& \propto \pi_{i,k} \prod_{r=1}^{R} \alpha_{k,r}^{R^W_{ir}}(1-\alpha_{k,r})^{F^W_{ir}}
|
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& \propto \pi_{i,k} \prod_{r=1}^{R} \alpha_{k,r}^{R_{ir}}(1-\alpha_{k,r})^{F_{ir}}
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
|
|
@ -821,33 +866,35 @@ p(Y_{\bullet,j}\mid W_j=r,\alpha,Z)&= \prod_{i=1}^{n_1} \alpha_{Z_i,r}^{Y_{i,j}}
|
|||
\end{align*}
|
||||
$$
|
||||
|
||||
On peut poser $R_{jq}^{Z} = \sum_{i=1}^{n_{1}}\mathbb{1}_{Z_{i}=q} Y_{i,j}$ et $F_{jq}^{Z} = \sum_{i=1}^{n_{1}}\mathbb{1}_{Z_{i}=q} (1-Y_{i,j})$ et on définit les matrices $\mathbf{R}^Z$ et $\mathbf{F}^{Z}$.
|
||||
**A MODIFIER**
|
||||
|
||||
On a :
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
p(W_{j}=r\mid Y_{\bullet,j},\alpha, Z, \rho) \propto \rho_{r}\prod_{q=1}^Q\alpha_{q,r}^{R^Z_{jq}}(1-\alpha_{q,r})^{F_{jq}^Z}
|
||||
\end{align*}
|
||||
\begin{align*}
|
||||
p(Z_{i}\mid P_{i}) & = \ilr^{-1}(P_{i}) = (\pi_{i,1},\dots,\pi_{i,k},\dots,\pi_{i,K}) \\
|
||||
p(Y_{i,\bullet}\mid Z_{i}, \alpha, W) & = \prod_{j=1}^{n_{2}} \alpha_{Z_{i},W_{j}}^{Y_{ij}}(1- \alpha_{Z_{i},W_{j}})^{1-Y_{ij}} \\
|
||||
p(Z_{i} = k \mid P_{i}) & = \pi_{i,k} \\
|
||||
p(Y_{i,\bullet}\mid Z_{i} = k, \alpha, W) & = \prod_{j=1}^{n_{2}} \prod_{r=1}^{R}\alpha_{k,r}^{\mathbb{1}_{W_{j} = r} Y_{ij}}(1- \alpha_{k,r})^{\mathbb{1}_{W_{j} = r}(1-Y_{ij})} \\
|
||||
& = \prod_{r=1}^{R} \alpha_{k,r}^{\sum_{j=1}^{n_{2}}W_{jr}Y_{ij}} (1-\alpha_{k,r})^{\sum_{j=1}^{n_{2}}W_{jr}(1-Y_{ij})}
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
À la fin
|
||||
En posant $R_{ir}=\sum_{j=1}^{n_{2}}W_{jr}Y_{ij}$ et $F_{ir}=\sum_{j=1}^{n_{2}}W_{jr}(1-Y_{ij})$ on définit les matrices $\mathbf{R}$ et $\mathbf{F}$ qui comptent les succès et échecs par ligne $i$ et groupe $r$.
|
||||
|
||||
$$
|
||||
W_{j} \sim \Cat_{R}(\tilde{\rho}_{1:R}^j)
|
||||
$$
|
||||
|
||||
### Implémentation
|
||||
Ce qui donne pour les $\tilde{\pi}_{i,k}$ de la posterior:
|
||||
|
||||
$$
|
||||
\begin{align*}
|
||||
\log \tilde{p_{jr}} & = \log \rho_{r} + \sum_{q=1}^{Q} [R_{jq}^{Z} \log\alpha_{q,r} + F_{jq}^W\log{(1-\alpha_{q,r})}] \\
|
||||
\tilde{\rho}_{jr} &= \frac{\exp(\log \tilde{p}_{jr} - m_{j})}{\sum_{l=1}^{R}\exp(\log \tilde{p_{jr}}-m_{j})},\quad m_{j} = \max_{l} \log p_{jr}
|
||||
\tilde{\pi}_{i,k} = p(Z_{i} = k\mid Y_{i,\bullet},\alpha,W,P_{i}) & \propto p(Y_{i,\bullet}\mid Z_{i} = k, \alpha, W, P_{i})p(Z_{i}=k\mid P_{i})\\
|
||||
& \propto \pi_{i,k} \prod_{r=1}^{R} \alpha_{k,r}^{R_{ir}}(1-\alpha_{k,r})^{F_{ir}}
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
Ainsi :
|
||||
Et ainsi à la fin :
|
||||
|
||||
$$
|
||||
\log \tilde{R} = \log(\rho) + \mathbf{R}^Z\log\alpha^{\top} + \mathbf{F}^Z \log(1-\alpha)^{\top}
|
||||
Z_{i}\mid P_{i}, Y, W, \alpha \sim \Cat_{K}(\tilde{\pi}_{i,1},\dots, \tilde{\pi}_{i,K})
|
||||
$$
|
||||
|
||||
## Loi de $\alpha \mid Y,Z,W$
|
||||
|
|
|
|||
|
|
@ -18,6 +18,4 @@ Exécution arrêtée
|
|||
```
|
||||
|
||||
- [ ] Essayer de reproduire l'erreur de `vapply` pour la réparer 🆔 ckx0ew
|
||||
+ Elle semble lier au fait d'ajouter des modèles `NULL`
|
||||
+ [ ] Ajouter la même suppression pour discarded que pour compared
|
||||
- [ ] Implémenter un test unitaire pour prévenir la régression ⛔ ckx0ew
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue