diff --git a/.obsidian/plugins/obsidian-livesync/data.json b/.obsidian/plugins/obsidian-livesync/data.json index 55cf143..cc32821 100644 --- a/.obsidian/plugins/obsidian-livesync/data.json +++ b/.obsidian/plugins/obsidian-livesync/data.json @@ -53,7 +53,7 @@ "syncInternalFilesIgnorePatterns": "\\/node_modules\\/, \\/\\.git\\/, \\/obsidian-livesync\\/", "syncInternalFilesTargetPatterns": "", "syncInternalFilesInterval": 60, - "additionalSuffixOfDatabaseName": "949e3f3f8b9f8e9a", + "additionalSuffixOfDatabaseName": "04d8e1f8f990135f", "ignoreVersionCheck": false, "lastReadUpdates": 25, "deleteMetadataOfDeletedFiles": false, @@ -68,14 +68,14 @@ "useDynamicIterationCount": false, "syncAfterMerge": false, "configPassphraseStore": "", - "encryptedPassphrase": "%$U76C/u2KmZ3FQ2VmzCSL1RK0VGHAL4znd0s5ihlDPC8qci/TAWBoNFN/TfO9qS6VPbFn3ApeXJbMnbF9SBg7evaeN6N+INEhxQ6VbfBFA/Bw8dt3jpnE+ENBSi8mpXlN4Q1DdEGdvDhl738BGqk=", - "encryptedCouchDBConnection": "%$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", + "encryptedPassphrase": "%$/SlHxiVtXtFU3c4at00gKGxrjW29N00XC98orq8AQ60xvd8vWexrUwcMLsCPSMz3XBFJ8is1NDMVP3fX1JOQSlpehq00+1qBEW542jBUEAMqsHwYLGLOcBAnzr+5zrHHoWXO9KbWRPoRlGa+9jQ=", + "encryptedCouchDBConnection": "%$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", "permitEmptyPassphrase": false, "remoteConfigurations": { "legacy-couchdb": { "id": "legacy-couchdb", "name": "CouchDB Remote", - "uri": "%$U76C/u2KmZ3FQ2VmzCSL1RK0VGHAL4znd0s5ihlDPC+sYELhS5zOuRx1QewULyFpDRLiGjOF/tA5YtckKZopgwD9WKP8UgqefQ4S+VgURG24fm7cbfB9zNiPsNTUJjHX8j7+62Osr8b0DcmiQxOHhxL2L7x7GDGdFMrZJg28wkP1QOAxV6CgI1z5g3OJomVDajCFJxEmajDG0WuWPkY/hd9b5MsB2FU3H3aAU11FafMSvBTcG8PiSbBuXuFRmq50sbpXNV8pMQ==", + "uri": "%$/SlHxiVtXtFU3c4at00gKGxrjW29N00XC98orq8AQ61et3xs0edjMOOOYl3YEJtOdOz5tXjD8qKiAdT1tGzh6Hj3f4jngdJxHVFGQayV1E8NSsCqhb0Y2qrh2j2x3FXyTAENB9YE361+t/tBwPaBjjcqXYd8DALMcZQXsjE554Bj5zt0AD2tGTvWpAiXXRHMSEzUshIyZqnqye/Gk++K7nSwPhdV4bwb2Wbkfsxn1OOupQrE3tVx968vO6k+gnrkc3j2aSptLw==", "isEncrypted": true } }, @@ -150,6 +150,7 @@ "P2P_turnServers": "", "P2P_turnUsername": "", "P2P_turnCredential": "", + "P2P_useDiagRTC": false, "doctorProcessedVersion": "0.25.27", "bucketCustomHeaders": "", "couchDB_CustomHeaders": "", diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 676aa61..c6e42a1 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -197,9 +197,19 @@ "icon": "quote-glyph", "title": "References" } + }, + { + "id": "6734703bbf1b5f03", + "type": "leaf", + "state": { + "type": "git-view", + "state": {}, + "icon": "git-pull-request", + "title": "Source Control" + } } ], - "currentTab": 7 + "currentTab": 8 } ], "direction": "horizontal", diff --git a/Thèse/Axes/Phylogénie/SBM avec covariance latente.md b/Thèse/Axes/Phylogénie/SBM avec covariance latente.md index 6d790e5..ce5f2e2 100644 --- a/Thèse/Axes/Phylogénie/SBM avec covariance latente.md +++ b/Thèse/Axes/Phylogénie/SBM avec covariance latente.md @@ -31,239 +31,192 @@ avec $\Sigma$, la matrice de variance-covariance déterminée en fonction de l'a \usepackage{amsmath,amssymb} -\usetikzlibrary{arrows.meta,positioning,shapes.geometric,calc} +\usetikzlibrary{ + +arrows.meta, + +positioning, + +shapes.geometric, + +calc, + +fit + +} + + \begin{document} + \begin{tikzpicture}[ + font=\sffamily, + >=Latex, -node distance=1.5cm and 2cm, + +node distance=1cm and 0.25cm, + 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 + +draw=gray!70, + +line width=0.9pt, + +align=center, + +inner sep=4pt + }, + 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}, -observed/.style={base,circle,fill=purple!8} + +observed/.style={base,circle,fill=purple!8}, + +plate/.style={ + +draw=black!60, + +rounded corners, + +inner sep=8pt + +} + ] + + %-------------------------------------------------- -% Hyperparameters rows + +% Row clustering + %-------------------------------------------------- + + + \node[prior] (sigma) {$\sigma^2$}; + \node[known,right=of sigma] (Sigma) {$\Sigma$}; + + \node[latent,below=of sigma] (Pi) {$P_i$}; -\node[latent,below=of Sigma] (Pip) {$P_{i'}$}; -\node[latent,below=of Pi] (Zi) {$Z_i$}; -\node[latent,below=of Pip] (Zip) {$Z_{i'}$}; +\node[latent,below=0.5cm of Pi] (Zi) {$Z_i$}; -%-------------------------------------------------- -% Hyperparameters columns -%-------------------------------------------------- -\node[prior,right=4cm of Sigma] (rho) {$\rho$}; + -\node[latent,below left=of rho] (Wj) {$W_j$}; -\node[latent,below right=of rho] (Wjp) {$W_{j'}$}; - -%-------------------------------------------------- -% Intercept -%-------------------------------------------------- -\node[prior] (alpha) -at ($(Zi)!0.5!(Wj)+(0,-3)$) -{$\alpha$}; - -%-------------------------------------------------- -% Observations -%-------------------------------------------------- -\node[observed] -at ($(Zi)!0.5!(Wj)+(0,-1.4)$) -(Yij) {$Y_{ij}$}; - -\node[observed] -at ($(Zi)!0.5!(Wjp)+(2.0,-1.4)$) -(Yijp) {$Y_{ij'}$}; - -\node[observed] -at ($(Zip)!0.5!(Wj)+(-2.0,-1.4)$) -(Yipj) {$Y_{i'j}$}; - -\node[observed] -at ($(Zip)!0.5!(Wjp)+(0,-1.4)$) -(Yipjp) {$Y_{i'j'}$}; - -%-------------------------------------------------- -% Row side -%-------------------------------------------------- \draw[directed] (sigma) -- (Pi); + \draw[directed] (Sigma) -- (Pi); -\draw[directed] (sigma) -- (Pip); -\draw[directed] (Sigma) -- (Pip); - \draw[directed] (Pi) -- (Zi); -\draw[directed] (Pip) -- (Zip); + + %-------------------------------------------------- -% Column side + +% Column clustering + %-------------------------------------------------- + +\node[latent,right=2.5cm of Zi] (Wj) {$W_j$}; + + + +\node[prior] (rho) at (Wj |- sigma) {$\rho$}; + + + \draw[directed] (rho) -- (Wj); -\draw[directed] (rho) -- (Wjp); + + %-------------------------------------------------- -% 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); +% Observation %-------------------------------------------------- -% Correlation structure + + + +\node[observed] (Yij) + +at ($(Zi)!0.5!(Wj)+(0,-0.9)$) + +{$Y_{ij}$}; + + + +\draw[directed] (Zi) -- (Yij); + +\draw[directed] (Wj) -- (Yij); + + + +\draw[bidirected] (Zi) -- (Wj); + + + %-------------------------------------------------- + +% Intercept + +%-------------------------------------------------- + + + +\node[prior] (alpha) + +at ($(Yij)+(0,-2.5)$) + +{$\alpha$}; + + + +\draw[directed] (alpha) -- (Yij); + + + \draw[bidirected] (alpha) -- (Zi); -\draw[bidirected] (alpha) -- (Zip); \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} - -\tikzset{ - -every path/.append style = { - -arrows = ->, - -> = stealth,}, - -every node/.append style = { - -shape = circle, - -draw = black, - -minimum size=3em - -}, - -latent/.style = { - -fill = lightgray - -}, - -prior/.style = { - -fill = red}, - -moral/.style = { - -dashed, - -> = {}, % remove arrow tip - -arrows = -, % ensure no arrows - -}} -\node (y) {$Y$}; +%-------------------------------------------------- + +% Plates + +%-------------------------------------------------- -\node[latent] (z) [above left = of y] {$Z$}; +\node[plate,fit=(Pi)(Zi),label={[align=center]left:$i=1,\ldots,n_1$}] {}; -\node[latent] (w) [above right = of y] {$W$}; +\node[plate,fit=(Wj),label={[align=center]right:$j=1,\ldots,n_2$}] {}; -\node[latent] (P) [above = of z] {$P$}; +\node[plate, + +fit=(Yij), + +label=below right:{$(i,j)$}] {}; -\node[prior] (sigma2) [above = of P] {$\sigma^2$}; - - - -\node[prior] (rho) [above = of w] {$\rho_{1:R}$}; - - - -\node[prior] (alpha) [below = of y] {$\boldsymbol{\alpha}$}; - - - -\path (z) edge (y); - - - -\path (w) edge (y); - - - -\path (rho) edge (w); - - - -\path (alpha) edge (y); - - - -\path (P) edge (z); - - - -\path (sigma2) edge (P); - - - -% moral - - - -\path[moral] (z) edge (alpha); - - - -\path[moral] (w) edge (alpha); - - - -\path[moral] (z) edge (w); - \end{tikzpicture} \end{document} @@ -643,14 +596,14 @@ $$ \end{align*} $$ -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 $r$. +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 $r$. Ce qui donne pour les $\tilde{\pi}_{i,k}$ de la posterior: $$ \begin{align*} \tilde{\pi}_{i,k} = p(Z_{i} = k\mid Y_{i,\bullet},\alpha,W,P_{i}) & \propto p(Y_{i,\bullet}\mid Z_{i} = k, \alpha, W, P_{i})p(Z_{i}=k\mid P_{i})\\ -& \propto \pi_{i,k} \prod_{r=1}^{R} \alpha_{k,r}^{R_{ir}}(1-\alpha_{k,r})^{F_{ir}} +& \propto \pi_{i,k} \prod_{r=1}^{R} \alpha_{k,r}^{R^W_{ir}}(1-\alpha_{k,r})^{F^W_{ir}} \end{align*} $$ @@ -864,6 +817,14 @@ p(Y_{\bullet,j}\mid W_j=r,\alpha,Z)&= \prod_{i=1}^{n_1} \alpha_{Z_i,r}^{Y_{i,j}} \end{align*} $$ +On peut poser $R_{jq}^{Z} = \sum_{i=1}^{n_{1}}\mathbb{1}_{Z_{i}=q} Y_{i,j}$ et $F_{jq}^{Z} = \sum_{i=1}^{n_{1}}\mathbb{1}_{Z_{i}=q} (1-Y_{i,j})$ et on définit les matrices $\mathbf{R}^Z$ et $\mathbf{F}^{Z}$. + +$$ + \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*} +$$ + **A MODIFIER** On a :