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vault backup: 2026-06-09 18:21:53

Browse source 
Affected files:
.obsidian/workspace.json
Thèse/Axes/Phylogénie/SBM avec covariance latente.md
This commit is contained in:
Louis 2026-06-09 18:21:53 +02:00
parent 4f2ed9a69c
commit 360c9ba327
2 changed files with 17 additions and 10 deletions
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6
.obsidian/workspace.json vendored
View file

@ -13,13 +13,13 @@
"state": {
"type": "markdown",
"state": {
"file": "Thèse/Lectures/@quericBridgingMaximumLikelihood2026.md",
"file": "Thèse/Axes/Phylogénie/SBM avec covariance latente.md",
"mode": "source",
"source": false,
"backlinks": false
},
"icon": "lucide-file",
"title": "@quericBridgingMaximumLikelihood2026"
"title": "SBM avec covariance latente"
}
}
]
@ -227,8 +227,8 @@
},
"active": "5a22d122169dedf7",
"lastOpenFiles": [
"@quericBridgingMaximumLikelihood2026.md",
"Thèse/Lectures/@quericBridgingMaximumLikelihood2026.md",
"@quericBridgingMaximumLikelihood2026.md",
"Thèse/Articles/Review papier colBiSBM.md",
"Résumé des tâches.md",
"Thèse/TODO/2026-05-18.md",

21
Thèse/Axes/Phylogénie/SBM avec covariance latente.md
View file

@ -801,12 +801,9 @@ observed/.style={base, circle, fill=purple!8,inner sep=1pt}]
\draw[directed] (rho) -- (Wjp);
\draw[directed] (Wj) -- (Ydotj);
\draw[directed] (Wjp) -- (Ydotjp);
\draw[directed] (Z) -- (Ydotj);
\draw[directed] (Z) -- (Ydotjp);
@ -851,13 +848,23 @@ Du DAG détaillé ci-dessus on peut déduire que pour chaque $Z_{i}$ on doit reg
$$
\begin{align*}
p(W_{j}\mid Y_{\bullet,j},\alpha,Z,\rho) &\propto p(Y_{\bullet,j}\mid W_{j},\alpha,Z,\rho)p(W_{j}\mid Z, \alpha, \rho) \\
& \propto p(Y_{\bullet,j}\mid W_j,\alpha,Z)p(W_j\mid\rho)
%& \propto p(Y_{i,\bullet}\mid Z_{i}, \alpha, W)p(Z_{i}\mid P_{i})
\end{align*}
$$
**A MODIFIER**
car $Y_{\bullet,j}\bot \rho\mid Z,\alpha,W_j$ et $W_j \bot Z,\alpha\mid\rho$
car $Z_{i}\bot(W,\alpha)\mid P_{i}$ et $Y_{i,\bullet}\bot P_{i}\mid Z_{i}$.
$$
\begin{align*}
p(W_j=r\mid \rho) &= \rho_r\\
p(Y_{\bullet,j}\mid W_j=r,\alpha,Z)&= \prod_{i=1}^{n_1} \alpha_{Z_i,r}^{Y_{i,j}}(1-\alpha_{Z_i,r})^{1-Y_{i,j}}\\
&= \prod_{q=1}^Q\prod_{i=1}^{n_1} \alpha_{q,r}^{\mathbb{1}_{Z_i=q}Y_{i,j}}(1-\alpha_{q,r})^{\mathbb{1}_{Z_i=q}(1-Y_{i,j})}\\
&= \prod_{q=1}^Q\alpha_{q,r}^{\sum_{i=1}^{n_1} \mathbb{1}_{Z_i=q}Y_{i,j}}(1-\alpha_{q,r})^{\sum_{i=1}^{n_1}\mathbb{1}_{Z_i=q}(1-Y_{i,j})}
\end{align*}
$$
**A MODIFIER**
On a :