From bc487291fa2e70aada04a05dcb1a695c6d73ef39 Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Mon, 15 Jul 2024 16:55:36 +0200 Subject: [PATCH] rapport : model selection ajout --- .../chapter4-simulations/model-selection.tex | 88 +- .../model_selection/model-selection.tex | 113 + .../inference/model-proportions.tex | 348 +-- .../model_selection/eps-pi-rho-preferred.tex | 2283 +++++++++++++++++ 4 files changed, 2590 insertions(+), 242 deletions(-) create mode 100644 tables/simulations/model_selection/model-selection.tex create mode 100644 tikz/simulations/model_selection/eps-pi-rho-preferred.tex diff --git a/rapport/chapter4-simulations/model-selection.tex b/rapport/chapter4-simulations/model-selection.tex index abb70ae..d5e7235 100644 --- a/rapport/chapter4-simulations/model-selection.tex +++ b/rapport/chapter4-simulations/model-selection.tex @@ -1,17 +1,15 @@ \section[Capacity to distinguish models]{Capacity to distinguish - $\pi\rho\text{-}colBiSBM$~from\newline$iid\text{-}colBiSBM$ and other + $\pi\rho\text{-}colBiSBM$~from\newline + $iid\text{-}colBiSBM$ and other models}\label{capacity-to-distinguish-pirhotext-colbisbm-from-iidtext-colbisbm-and-other-variants} - The idea of this model selection simulations is to assess how the model select the correct \emph{colBiSBM} model among the possible ones: \textit{iid, pi, rho, pirho}. This difference being based on the row and -col block proportions. - +col block proportions.\\ For this task we choose the same simulation settings as -\cite{chabert-liddellLearningCommonStructures2024a}. - -Namely $n_{1}^{m} = 90, n_{2}^{m} = 90, Q_1 = Q_2 = 3$, -$\bm{\alpha}, \bm{\pi}$ and $\bm{\rho}$ are set as follows: +\cite{chabert-liddellLearningCommonStructures2024a}.\\ +Namely, $n_{1}^{m} = 90, n_{2}^{m} = 90, Q_1 = Q_2 = 3$, +$\bm{\alpha}, \bm{\pi}$ and $\bm{\rho}$ are set as follows:\\ \begin{minipage}[l]{0.4\linewidth} \begin{align*} \bm{\alpha} =.25 + \begin{pmatrix} @@ -38,7 +36,8 @@ $\bm{\alpha}, \bm{\pi}$ and $\bm{\rho}$ are set as follows: \end{minipage} with $\eps[\alpha] = 0.16$, $\eps[\pi]$ and $\eps[\rho]$ taking 9 values equally spaced in -$\left[ 0, .28\right]$. We simulate 324 different collections for each +$\left[ 0, .28\right]$.\newline +We simulate 324 different collections for each value of $\eps[\pi]$ and $\eps[\rho]$. $\pi\rho\text{-}colBiSBM$, $\pi\text{-}colBiSBM$, @@ -56,73 +55,26 @@ $\bm{\pi}^1 \neq \bm{\pi}^2$ and $\eps[\rho] > 0$ or $\bm{\rho}^1 \neq \bm{\rho}^2$, the model is a $\pi\rho\text{-}colBiSBM$. -\begin{table}[!h] - - \caption{\label{tab:tables}\label{tab:pi-model-sel}Model selection for varying $\pi$ mixture parameters} - \centering - \begin{tabular}[t]{lccccl} - \toprule - \multicolumn{1}{c}{ } & \multicolumn{4}{c}{Models} & \multicolumn{1}{c}{Blocks} \\ - \cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6} - $\eps[\pi]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_1$ \\ - \midrule - 0.00 & 0.65 & 0.00 & 0.35 & 0.00 & 3 \\ - 0.04 & 0.66 & 0.00 & 0.34 & 0.00 & 3 \\ - 0.07 & 0.64 & 0.01 & 0.34 & 0.01 & 3.01 $\pm$ 0.01 \\ - 0.11 & 0.63 & 0.03 & 0.31 & 0.03 & 3.01 $\pm$ 0.01 \\ - 0.14 & 0.55 & 0.12 & 0.28 & 0.05 & 3 \\ - \addlinespace - 0.18 & 0.39 & 0.26 & 0.21 & 0.13 & 3.01 \\ - 0.21 & 0.23 & 0.42 & 0.13 & 0.23 & 3.01 \\ - 0.25 & 0.10 & 0.56 & 0.05 & 0.29 & 3.02 $\pm$ 0.01 \\ - 0.28 & 0.01 & 0.65 & 0.01 & 0.33 & 3.01 $\pm$ 0.01 \\ - \bottomrule - \end{tabular} -\end{table} - -\begin{table}[!h] - - \caption{\label{tab:tables}\label{tab:rho-model-sel}Model selection for varying $\rho$ mixture parameters} - \centering - \begin{tabular}[t]{lccccl} - \toprule - \multicolumn{1}{c}{ } & \multicolumn{4}{c}{Models} & \multicolumn{1}{c}{Blocks} \\ - \cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6} - $\eps[\rho]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_2$ \\ - \midrule - 0.00 & 0.63 & 0.37 & 0.00 & 0.00 & 3 \\ - 0.04 & 0.65 & 0.34 & 0.00 & 0.01 & 3 \\ - 0.07 & 0.64 & 0.33 & 0.01 & 0.01 & 3 \\ - 0.11 & 0.64 & 0.31 & 0.03 & 0.02 & 3 \\ - 0.14 & 0.53 & 0.29 & 0.11 & 0.06 & 3 \\ - \addlinespace - 0.18 & 0.42 & 0.20 & 0.24 & 0.14 & 3.01 \\ - 0.21 & 0.25 & 0.12 & 0.40 & 0.22 & 3.01 \\ - 0.25 & 0.08 & 0.06 & 0.58 & 0.29 & 3.01 \\ - 0.28 & 0.01 & 0.01 & 0.65 & 0.32 & 3 \\ - \bottomrule - \end{tabular} -\end{table} +\input{../tables/simulations/model_selection/model-selection.tex} \begin{figure}[H] - % \includegraphics{./Rcodes/simulation/img/plot_model_function_eps.png} - \caption{Plot of preferred model in function of $\eps[\pi]$ and $\eps[\rho]$} - \label{fig:pref_model_func_eps} + \centering + \input{../tikz/simulations/model_selection/eps-pi-rho-preferred.tex} + \caption{\label{fig:pref_model_func_eps}Plot of model selection proportions + over the different datasets in + function of $\eps[\pi]$ and $\eps[\rho]$} \end{figure} \paragraph{Results:} -On the figure \ref{fig:pref_model_func_eps} and tables -\ref{tab:pi-model-sel} and \ref{tab:rho-model-sel}, one can see that +On the figure \ref{fig:pref_model_func_eps} and table \ref{tab:model-selection}, one can see that there is a turning point around $\eps[\pi] = 0.2$ (resp. $\eps[\rho] = 0.2$), before which $iid\text{-}colBiSBM$ and $\rho\text{-}colBiSBM$ (resp. $\pi\text{-}colBiSBM$) are selected -most of the times and after $0.2$ the $\pi\text{-}colBiSBM$ (resp. +very often and after $0.2$ the $\pi\text{-}colBiSBM$ (resp. $\rho\text{-}colBiSBM$) and $\pi\rho\text{-}colBiSBM$ gets more and -more selected, highlighting our capacity to recover the simulated -structure. +more selected. Moreover, the number of blocks are correctly detected in most +of the case. -\paragraph*{Remark:} - -Please note that when ``Recovered $Q_1$(or $Q_2$)'' is not an -integer it's because some procedures returned a value other than 3. +These two results highlight our capacity to recover the simulated +structure. \ No newline at end of file diff --git a/tables/simulations/model_selection/model-selection.tex b/tables/simulations/model_selection/model-selection.tex new file mode 100644 index 0000000..7db3b82 --- /dev/null +++ b/tables/simulations/model_selection/model-selection.tex @@ -0,0 +1,113 @@ +\begin{table} + \centering + \caption{\label{tab:model-selection}Filtered block recovery and model selection proportions} + \centering + \resizebox{\ifdim\width>\linewidth\linewidth\else\width\fi}{!}{ + \begin{tabular}[t]{llllllllll|>{}llll} + \toprule + \multicolumn{2}{c}{ } & \multicolumn{8}{c}{Block number recovery} & \multicolumn{4}{c}{Model selection proportions} \\ + \cmidrule(l{3pt}r{3pt}){3-10} \cmidrule(l{3pt}r{3pt}){11-14} + \multicolumn{2}{c}{ } & \multicolumn{2}{c}{$iid$} & \multicolumn{2}{c}{$\pi$} & \multicolumn{2}{c}{$\rho$} & \multicolumn{2}{c}{$\pi\rho$} & \multicolumn{4}{c}{ } \\ + \cmidrule(l{3pt}r{3pt}){3-4} \cmidrule(l{3pt}r{3pt}){5-6} \cmidrule(l{3pt}r{3pt}){7-8} \cmidrule(l{3pt}r{3pt}){9-10} + $\epsilon_{\pi}$ & $\epsilon_{\rho}$ & $\mathbbb{1}_{\widehat{Q_1}_{iid}=3}$ & $\mathbbb{1}_{\widehat{Q_2}_{iid}=3}$ & $\mathbbb{1}_{\widehat{Q_1}_{\pi}=3}$ & $\mathbbb{1}_{\widehat{Q_2}_{\pi}=3}$ & $\mathbbb{1}_{\widehat{Q_1}_{\rho}=3}$ & $\mathbbb{1}_{\widehat{Q_2}_{\rho}=3}$ & $\mathbbb{1}_{\widehat{Q_1}_{\pi\rho}=3}$ & $\mathbbb{1}_{\widehat{Q_2}_{\pi\rho}=3}$ & $iid$ & $\pi$ & $\rho$ & $\pi\rho$ \\ + \midrule + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.991 & 0.009 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & & \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.981 & & 0.019 & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.917 & & 0.083 & \\ + \cmidrule{2-14} + & 0.210 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.361 & & 0.630 & 0.009 \\ + \cmidrule{2-14} + & 0.245 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.111 & & 0.889 & \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.000} & 0.280 & 1 & 1 & 1 & 0.991 & 1 & 1 & 1 & 1 & 0.009 & 0.009 & 0.963 & 0.019 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.981 & 0.009 & 0.009 & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.981 & 0.019 & & \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.991 & & 0.009 & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.935 & & 0.065 & \\ + \cmidrule{2-14} + & 0.210 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.454 & & 0.546 & \\ + \cmidrule{2-14} + & 0.245 & 1 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & 0.157 & & 0.843 & \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.035} & 0.280 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.019 & & 0.972 & 0.009 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.991 & 0.009 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.972 & 0.019 & 0.009 & \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.972 & 0.019 & 0.009 & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.880 & 0.056 & 0.065 & \\ + \cmidrule{2-14} + & 0.210 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.324 & & 0.648 & 0.028 \\ + \cmidrule{2-14} + & 0.245 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.139 & & 0.843 & 0.019 \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.070} & 0.280 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.019 & & 0.963 & 0.019 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.917 & 0.083 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.917 & 0.065 & 0.019 & \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.935 & 0.056 & 0.009 & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.806 & 0.056 & 0.139 & \\ + \cmidrule{2-14} + & 0.210 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.333 & 0.019 & 0.593 & 0.056 \\ + \cmidrule{2-14} + & 0.245 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.102 & & 0.843 & 0.056 \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.105} & 0.280 & 1 & 1 & 1 & 0.991 & 1 & 1 & 1 & 1 & 0.037 & & 0.935 & 0.028 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.296 & 0.704 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.370 & 0.620 & & 0.009 \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.343 & 0.657 & & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.343 & 0.546 & 0.037 & 0.074 \\ + \cmidrule{2-14} + & 0.210 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.148 & 0.269 & 0.176 & 0.407 \\ + \cmidrule{2-14} + & 0.245 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.037 & 0.065 & 0.324 & 0.574 \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.210} & 0.280 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & & 0.417 & 0.583 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.148 & 0.852 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.157 & 0.843 & & \\ + \cmidrule{2-14} + & 0.070 & 1 & 1 & 1 & 1 & 0.991 & 1 & 1 & 1 & 0.148 & 0.852 & & \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.139 & 0.833 & & 0.028 \\ + \cmidrule{2-14} + & 0.210 & 1 & 0.981 & 1 & 1 & 1 & 1 & 1 & 1 & 0.028 & 0.343 & 0.111 & 0.519 \\ + \cmidrule{2-14} + & 0.245 & 1 & 1 & 1 & 1 & 0.991 & 1 & 1 & 1 & & 0.130 & 0.083 & 0.787 \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.245} & 0.280 & 0.991 & 0.991 & 1 & 1 & 0.991 & 1 & 1 & 1 & 0.009 & 0.037 & 0.111 & 0.843 \\ + \cmidrule{1-14} + & 0.000 & 1 & 1 & 1 & 1 & 1 & 1 & 0.991 & 1 & 0.019 & 0.981 & & \\ + \cmidrule{2-14} + & 0.035 & 1 & 1 & 1 & 1 & 1 & 1 & 0.981 & 1 & 0.046 & 0.954 & & \\ + \cmidrule{2-14} + & 0.070 & 1 & 0.991 & 1 & 0.991 & 0.991 & 1 & 0.991 & 0.981 & 0.019 & 0.954 & & 0.028 \\ + \cmidrule{2-14} + & 0.105 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0.019 & 0.898 & & 0.083 \\ + \cmidrule{2-14} + & 0.210 & 0.981 & 0.991 & 1 & 1 & 1 & 1 & 1 & 1 & & 0.435 & 0.009 & 0.556 \\ + \cmidrule{2-14} + & 0.245 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & & 0.167 & 0.019 & 0.815 \\ + \cmidrule{2-14} + \multirow[t]{-7}{*}[6\dimexpr\aboverulesep+\belowrulesep+\cmidrulewidth]{\raggedright\arraybackslash 0.280} & 0.280 & 1 & 0.991 & 1 & 1 & 1 & 1 & 0.991 & 1 & & 0.019 & 0.028 & 0.954 \\ + \bottomrule + \end{tabular}} 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join=round] (127.80, 72.28) -- - (127.80,250.77); +\path[draw=drawColor,line width= 0.6pt,line join=round] (127.80, 39.47) -- + (127.80,211.31); -\path[draw=drawColor,line width= 0.6pt,line join=round] (146.03, 72.28) -- - (146.03,250.77); +\path[draw=drawColor,line width= 0.6pt,line join=round] (145.35, 39.47) -- + (145.35,211.31); -\path[draw=drawColor,line width= 0.6pt,line join=round] (164.26, 72.28) -- - (164.26,250.77); +\path[draw=drawColor,line width= 0.6pt,line join=round] (162.90, 39.47) -- + (162.90,211.31); -\path[draw=drawColor,line width= 0.6pt,line join=round] (182.49, 72.28) -- - (182.49,250.77); +\path[draw=drawColor,line width= 0.6pt,line join=round] (180.46, 39.47) -- + (180.46,211.31); -\path[draw=drawColor,line width= 0.6pt,line join=round] (200.72, 72.28) -- - (200.72,250.77); +\path[draw=drawColor,line width= 0.6pt,line join=round] (198.01, 39.47) -- + (198.01,211.31); \definecolor{drawColor}{RGB}{86,180,233} \definecolor{fillColor}{RGB}{86,180,233} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 46.67, 80.39) rectangle ( 63.08,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 49.69, 47.28) rectangle ( 65.49,203.50); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 64.90,202.09) rectangle ( 81.31,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 67.24,178.91) rectangle ( 83.04,203.50); \definecolor{drawColor}{RGB}{86,180,233} \definecolor{fillColor}{RGB}{86,180,233} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 64.90,117.95) rectangle ( 81.31,202.09); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 67.24, 92.12) rectangle ( 83.04,178.91); \definecolor{drawColor}{RGB}{0,158,115} \definecolor{fillColor}{RGB}{0,158,115} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 64.90,107.44) rectangle ( 81.31,117.95); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 67.24, 77.66) rectangle ( 83.04, 92.12); \definecolor{drawColor}{RGB}{240,228,66} \definecolor{fillColor}{RGB}{240,228,66} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 64.90, 92.41) rectangle ( 81.31,107.44); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 67.24, 66.08) rectangle ( 83.04, 77.66); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 64.90, 80.39) rectangle ( 81.31, 92.41); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 67.24, 47.28) rectangle ( 83.04, 66.08); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 83.13,236.64) rectangle ( 99.54,242.65); -\definecolor{drawColor}{RGB}{86,180,233} -\definecolor{fillColor}{RGB}{86,180,233} - -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 83.13,235.14) rectangle ( 99.54,236.64); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 84.79,200.61) rectangle (100.59,203.50); \definecolor{drawColor}{RGB}{0,158,115} \definecolor{fillColor}{RGB}{0,158,115} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 83.13,214.11) rectangle ( 99.54,235.14); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 84.79,181.80) rectangle (100.59,200.61); \definecolor{drawColor}{RGB}{240,228,66} \definecolor{fillColor}{RGB}{240,228,66} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 83.13,205.09) rectangle ( 99.54,214.11); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 84.79,173.12) rectangle (100.59,181.80); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 83.13, 80.39) rectangle ( 99.54,205.09); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] ( 84.79, 47.28) rectangle (100.59,173.12); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (101.36,236.64) rectangle (117.77,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (102.35,197.71) rectangle (118.14,203.50); \definecolor{drawColor}{RGB}{0,158,115} \definecolor{fillColor}{RGB}{0,158,115} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (101.36,233.64) rectangle (117.77,236.64); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (102.35,196.27) rectangle (118.14,197.71); +\definecolor{drawColor}{RGB}{240,228,66} +\definecolor{fillColor}{RGB}{240,228,66} + +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (102.35,194.82) rectangle (118.14,196.27); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (101.36, 80.39) rectangle (117.77,233.64); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (102.35, 47.28) rectangle (118.14,194.82); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (119.59,236.64) rectangle (136.00,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (119.90,193.37) rectangle (135.70,203.50); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (119.59, 80.39) rectangle (136.00,236.64); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (119.90, 47.28) rectangle (135.70,193.37); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (137.83,235.14) rectangle (154.23,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (137.45,199.16) rectangle (153.25,203.50); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (137.83, 80.39) rectangle (154.23,235.14); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (137.45, 47.28) rectangle (153.25,199.16); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (156.06,233.64) rectangle (172.46,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (155.00,194.82) rectangle (170.80,203.50); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (156.06, 80.39) rectangle (172.46,233.64); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (155.00, 47.28) rectangle (170.80,194.82); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (174.29,235.14) rectangle (190.70,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (172.56,196.27) rectangle (188.35,203.50); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (174.29, 80.39) rectangle (190.70,235.14); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (172.56, 47.28) rectangle (188.35,196.27); \definecolor{drawColor}{RGB}{230,159,0} \definecolor{fillColor}{RGB}{230,159,0} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (192.52,238.15) rectangle (208.93,242.65); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (190.11,194.82) rectangle (205.91,203.50); \definecolor{drawColor}{RGB}{0,114,178} \definecolor{fillColor}{RGB}{0,114,178} -\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (192.52, 80.39) rectangle (208.93,238.15); +\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (190.11, 47.28) rectangle (205.91,194.82); \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 0.00) rectangle (289.08,216.81); \definecolor{drawColor}{gray}{0.30} -\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61, 77.36) {0.00}; +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 36.93, 44.25) {0.00}; -\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61,117.93) {0.25}; +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 36.93, 83.30) {0.25}; -\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61,158.49) {0.50}; +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 36.93,122.36) {0.50}; -\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61,199.06) {0.75}; +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 36.93,161.41) {0.75}; -\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61,239.62) {1.00}; +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 36.93,200.47) {1.00}; \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 0.00) rectangle (289.08,216.81); \definecolor{drawColor}{gray}{0.20} -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81, 80.39) -- - ( 38.56, 80.39); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 39.13, 47.28) -- + ( 41.88, 47.28); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81,120.96) -- - ( 38.56,120.96); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 39.13, 86.33) -- + ( 41.88, 86.33); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81,161.52) -- - ( 38.56,161.52); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 39.13,125.39) -- + ( 41.88,125.39); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81,202.09) -- - ( 38.56,202.09); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 39.13,164.44) -- + ( 41.88,164.44); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81,242.65) -- - ( 38.56,242.65); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 39.13,203.50) -- + ( 41.88,203.50); \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 0.00) rectangle (289.08,216.81); \definecolor{drawColor}{gray}{0.20} -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 54.87, 69.53) -- - ( 54.87, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 57.59, 36.72) -- + ( 57.59, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 73.10, 69.53) -- - ( 73.10, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 75.14, 36.72) -- + ( 75.14, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] ( 91.33, 69.53) -- - ( 91.33, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] ( 92.69, 36.72) -- + ( 92.69, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (109.57, 69.53) -- - (109.57, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (110.25, 36.72) -- + (110.25, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (127.80, 69.53) -- - (127.80, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (127.80, 36.72) -- + (127.80, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (146.03, 69.53) -- - (146.03, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (145.35, 36.72) -- + (145.35, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (164.26, 69.53) -- - (164.26, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (162.90, 36.72) -- + (162.90, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (182.49, 69.53) -- - (182.49, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (180.46, 36.72) -- + (180.46, 39.47); -\path[draw=drawColor,line width= 0.6pt,line join=round] (200.72, 69.53) -- - (200.72, 72.28); +\path[draw=drawColor,line width= 0.6pt,line join=round] (198.01, 36.72) -- + (198.01, 39.47); \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 0.00) rectangle (289.08,216.81); \definecolor{drawColor}{gray}{0.30} -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 52.73, 48.63) {0.00}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 55.44, 15.82) {0.00}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 70.96, 48.63) {0.03}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 73.00, 15.82) {0.03}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 89.19, 48.63) {0.06}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 90.55, 15.82) {0.06}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (107.42, 48.63) {0.09}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (108.10, 15.82) {0.09}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (125.66, 48.63) {0.12}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (125.66, 15.82) {0.12}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (143.89, 48.63) {0.15}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (143.21, 15.82) {0.15}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (162.12, 48.63) {0.18}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (160.76, 15.82) {0.18}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (180.35, 48.63) {0.21}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (178.31, 15.82) {0.21}; -\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (198.58, 48.63) {0.24}; +\node[text=drawColor,rotate=-45.00,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at (195.87, 15.82) {0.24}; \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 0.00) rectangle (289.08,216.81); \definecolor{drawColor}{RGB}{0,0,0} -\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.10] at (127.80, 40.45) {$\epsilon_{\alpha}$}; +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.10] at (127.80, 7.64) {$\epsilon_{\alpha}$}; \end{scope} \begin{scope} -\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08); +\path[clip] ( 0.00, 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30.69) rectangle (356.90, 60.35); +\definecolor{drawColor}{gray}{0.92} + +\path[draw=drawColor,line width= 0.3pt,line join=round] (327.23, 45.52) -- + (356.90, 45.52); + +\path[draw=drawColor,line width= 0.6pt,line join=round] (327.23, 32.03) -- + (356.90, 32.03); + +\path[draw=drawColor,line width= 0.6pt,line join=round] (327.23, 59.00) -- + (356.90, 59.00); + +\path[draw=drawColor,line width= 0.6pt,line join=round] (342.07, 30.69) -- + (342.07, 60.35); +\definecolor{fillColor}{RGB}{86,180,233} + +\path[fill=fillColor] (330.94, 58.50) rectangle (353.19, 59.00); +\definecolor{fillColor}{RGB}{0,158,115} + +\path[fill=fillColor] (330.94, 32.03) rectangle (353.19, 58.50); +\end{scope} +\begin{scope} +\path[clip] ( 45.90,341.68) rectangle (356.90,374.83); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (201.40,363.51) {$\epsilon_{\pi}$}; +\end{scope} +\begin{scope} +\path[clip] ( 45.90,341.68) rectangle ( 75.57,374.83); 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sep=0pt, scale= 0.88] at (201.40,346.94) {0.14}; +\end{scope} +\begin{scope} +\path[clip] (221.74,341.68) rectangle (251.40,374.83); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (236.57,346.94) {0.175}; +\end{scope} +\begin{scope} +\path[clip] (256.90,341.68) rectangle (286.57,374.83); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (271.73,346.94) {0.21}; +\end{scope} +\begin{scope} +\path[clip] (292.07,341.68) rectangle (321.73,374.83); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (306.90,346.94) {0.245}; +\end{scope} +\begin{scope} +\path[clip] (327.23,341.68) rectangle (356.90,374.83); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (342.07,346.94) {0.28}; +\end{scope} +\begin{scope} +\path[clip] 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rectangle (390.04,236.19); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,rotate=-90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (362.16,221.35) {0.175}; +\end{scope} +\begin{scope} +\path[clip] (356.90,171.35) rectangle (390.04,201.02); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,rotate=-90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (362.16,186.19) {0.14}; +\end{scope} +\begin{scope} +\path[clip] (356.90,136.19) rectangle (390.04,165.85); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,rotate=-90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (362.16,151.02) {0.105}; +\end{scope} +\begin{scope} +\path[clip] (356.90,101.02) rectangle (390.04,130.69); +\definecolor{drawColor}{gray}{0.10} + +\node[text=drawColor,rotate=-90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 0.88] at (362.16,115.85) {0.07}; +\end{scope} +\begin{scope} +\path[clip] (356.90, 65.85) rectangle (390.04, 95.52); 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{0}; + +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.60] at ( 40.95, 92.10) {1}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{gray}{0.30} + +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.60] at ( 40.95, 29.97) {0}; + +\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.60] at ( 40.95, 56.94) {1}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,rotate= 90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.10] at ( 33.06,186.19) {Selection proportion}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.10] at (406.54,221.28) {Model}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{fillColor}{RGB}{86,180,233} + +\path[fill=fillColor] (407.26,186.52) rectangle (420.29,199.55); +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{fillColor}{RGB}{0,158,115} + +\path[fill=fillColor] (407.26,172.06) rectangle (420.29,185.09); +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{fillColor}{RGB}{240,228,66} + +\path[fill=fillColor] (407.26,157.61) rectangle (420.29,170.64); +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{fillColor}{RGB}{0,114,178} + +\path[fill=fillColor] (407.26,143.15) rectangle (420.29,156.19); +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (426.50,204.46) {sep}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (426.50,190.00) {iid}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (426.50,175.55) {$\pi$}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (426.50,161.09) {$\rho$}; +\end{scope} +\begin{scope} +\path[clip] ( 0.00, 0.00) rectangle (469.75,397.48); +\definecolor{drawColor}{RGB}{0,0,0} + +\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (426.50,146.64) {$\pi\rho$}; +\end{scope} +\end{tikzpicture}