rapport : ajout des simus d'inférences et de sélection de modèles
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12 changed files with 800 additions and 16 deletions
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@ -9,6 +9,7 @@ performances and the clustering capacities.
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the report repository at
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\url{https://gitea.polarolouis.fr/polarolouis/rapport-CEI-MIA-2023}.
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% \include{Rcodes/simulation/inference_analyze}
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% \include{Rcodes/simulation/model_selection_analyze}
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\input{chapter4-simulations/inference.tex}
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\input{chapter4-simulations/model-selection}
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% \include{Rcodes/simulation/netclustering_analyze}
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122
rapport/chapter4-simulations/inference.tex
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rapport/chapter4-simulations/inference.tex
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\section{Efficiency of the inference}
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The goal here is to assess the quality of the inference procedure.
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\paragraph{Simulation settings} For this simulation the data is simulated with
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$M = 2, n_{1}^{m} = 120, n_{2}^{m} = 120, Q_1 = Q_2 = 4$, $\bm{\alpha}, \bm{\pi}$
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and $\bm{\rho}$ are set as follows:
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\begin{align*}
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& \bm{\alpha} = .25 +
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\begin{pmatrix}
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3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] & - \eps[\alpha] \\
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2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] & \eps[\alpha] \\
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\eps[\alpha] & - \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha] \\
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- \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha] & 0
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\end{pmatrix},
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\end{align*}
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\begin{align*}
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\bm{\pi}^1 = \sigma_1
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\begin{pmatrix}
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0.2 & 0.4 & 0.4 & 0
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\end{pmatrix},
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& & \bm{\pi}^2 =
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\begin{pmatrix}
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0.25 & 0.25 & 0.25 & 0.25
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\end{pmatrix}, \\
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\bm{\rho}^1 =
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\begin{pmatrix}
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0.25 & 0.25 & 0.25 & 0.25
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\end{pmatrix}, & &
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\bm{\rho}^2 = \sigma_2
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\begin{pmatrix}
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0 & 0.33 & 0.33 & 0.33
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\end{pmatrix}, & &
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\end{align*}
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with $\eps[\alpha]$ taking nine equally spaced values ranging from 0 to 0.24.
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For each value of $\eps[\alpha]$, 108 datasets ($X_1, X_2$) are simulated,
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resulting in $9 \times 108 = 972$ datasets. More precisely, for each dataset,
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we pick uniformly at random two permutations of $\{ 1, \dots , 4 \}$
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($\sigma_1, \sigma_2$) with the constraint that $\sigma_1(4) \neq \sigma_2(1)$.
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This ensures that each of the two networks have a non-empty block that is empty
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in the other one. Then the networks are simulated with
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$\mathcal{B}$ern-$BiSBM_{120,120}(Q_1 = 4, Q_2 = 4,
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\bm{\alpha}, \bm{\pi}^m, \bm{\rho}^m)$
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with the previous parameters. Each network has 2 blocks in common and their
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connectivity structures encompass a mix of core-periphery, assortative
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community and disassortative community structures, depending on which 3 of the 4
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blocks are selected for each network. $\eps[\alpha]$ represents the strength of
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these structures, the larger, the easier it is to tell apart one block from
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another.
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The true model of all the simulation is a $\pi\rho\text{-}colBiSBM$.
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\paragraph{Inference} We want to measure the quality of the
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inference procedure, for this we use the inference described in the section
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\ref{sec:variational-estimation-of-the-parameters}.
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\paragraph{Quality indicators} To assess the quality of the inference, we will
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use the following indicators:
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\begin{itemize}
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\item First, for each dataset, we put in competition $\pi\text{-}colBiSBM$ with
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$sep\text{-}BiSBM$, $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$,
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$\pi\rho\text{-}colBiSBM$
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respectively. To do so, for each dataset, we compute the
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BIC-L of each model $\pi\text{-}colBiSBM$ is preferred to $sep\text{-}BiSBM$
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(resp. $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$,
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$\pi\rho\text{-}colBiSBM$) if
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its BIC-L is greater.
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\item When considering our \emph{colBiSBM} models we compare
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$\widehat{Q_1}$, $\widehat{Q_2}$ to
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their true values. ($Q_1 = 4$ and $Q_2 = 4$)
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\item Finally, we assess the quality of the node grouping by computing the
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Adjusted Rand Index \parencite{hubertComparingPartitions1985}, ARI = 0
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for a random grouping, ARI = 1 for a perfect recovery. For each
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network, for the
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$\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$,
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$\pi\rho\text{-}colBiSBM$ we compare the inferred block memberships to
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the real ones by computing the mean of the ARI per axis over the two
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networks
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\begin{equation*}
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\overline{\text{ARI}}_d = \frac{1}{2} \text{ARI}\big( \text{ARI}(\widehat{\bm{Z}^1_d},\bm{Z}^1_d) + \text{ARI}(\widehat{\bm{Z}^2_d},\bm{Z}^2_d) \big),
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\end{equation*}
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where $d$ is the dimension or axis (i.e., rows, $d=1$, or columns, $d=2$) of
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the block memberships.
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And we compute the ARI of the whole set of nodes to account for block
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pairing between networks
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\begin{equation*}
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\text{ARI}_d = \text{ARI}\big((\widehat{\bm{Z}^1_d},\widehat{\bm{Z}^2_d}),(\bm{Z}^1_d,\bm{Z}^2_d) \big).
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\end{equation*}
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\end{itemize}
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All these quality indicators are averaged over the 108 datasets. The results are
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provided in the tables \ref{tab:per_model_sep} to \ref{tab:per_model_pirho}. Each line corresponds to the
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108 datasets for a given value of value of $\eps[\alpha]$.
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\begin{figure}[ht]
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\centering
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\input{../tikz/simulations/inference/model-proportions.tex}
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\caption{Preferred model proportions over all datasets in function of
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$\eps[\alpha]$}
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\label{fig:prop-modele-pref}
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\end{figure}
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\foreach \modelname in {sep,iid,pi,rho,pirho}{
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\input{../tables/simulations/inference/\modelname.tex}
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}
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\paragraph{Results}
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For the model comparison, when $\eps[\alpha]$ is small
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($\eps[\alpha]\in[0, .04]$), the simulation model is close to the
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Erd\H{o}s-Reńyi network and it is very hard to find any structure beyond the one
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of a single block on each dimension.
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On the figure \ref{fig:inference-proportion-preferred} and table
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\ref{tab:proportion-preferred-table} we can see that from
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$\eps[\alpha] = 0.06$ around $70\%$ of the time the $\pi\rho\text{-}colBiSBM$
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model (i.e., the correct one) is selected.
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An interesting result we can read in the tables is that our models outperform
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the $sep\text{-}BiSBM$ when considering the ARI on the whole set of nodes
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($\text{ARI}_d$). This means that our models are able to recover the block
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pairing \emph{between the networks} in addition to recovering the blocks and
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their parameters.
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\clearpage
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128
rapport/chapter4-simulations/model-selection.tex
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rapport/chapter4-simulations/model-selection.tex
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\section[Capacity to distinguish models]{Capacity to distinguish
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$\pi\rho\text{-}colBiSBM$~from\newline$iid\text{-}colBiSBM$ and other
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models}\label{capacity-to-distinguish-pirhotext-colbisbm-from-iidtext-colbisbm-and-other-variants}
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The idea of this model selection simulations is to assess how the model
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select the correct \emph{colBiSBM} model among the possible ones:
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\textit{iid, pi, rho, pirho}. This difference being based on the row and
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col block proportions.
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For this task we choose the same simulation settings as
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\cite{chabert-liddellLearningCommonStructures2024a}.
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Namely $n_{1}^{m} = 90, n_{2}^{m} = 90, Q_1 = Q_2 = 3$,
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$\bm{\alpha}, \bm{\pi}$ and $\bm{\rho}$ are set as follows:
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\begin{minipage}[l]{0.4\linewidth}
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\begin{align*}
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\bm{\alpha} =.25 + \begin{pmatrix}
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3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] \\
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2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] \\
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\eps[\alpha] & - \eps[\alpha] & \eps[\alpha]
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\end{pmatrix},
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\end{align*}
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\end{minipage}
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\hfill
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\begin{minipage}[r]{0.4\linewidth}
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\begin{align*}
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\bm{\pi}^1 = \begin{pmatrix}
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\frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
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\end{pmatrix}, & & \bm{\pi}^2 = \sigma\begin{pmatrix}
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\frac{1}{3} - \eps[\pi], & \frac{1}{3}, & \frac{1}{3} + \eps[\pi]
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\end{pmatrix}, \\
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\bm{\rho}^1 = \begin{pmatrix}
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\frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
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\end{pmatrix}, & & \bm{\rho}^2 = \sigma\begin{pmatrix}
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\frac{1}{3} - \eps[\rho], & \frac{1}{3}, & \frac{1}{3} + \eps[\rho]
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\end{pmatrix},
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\end{align*}
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\end{minipage}
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with $\eps[\alpha] = 0.16$, $\eps[\pi]$ and
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$\eps[\rho]$ taking 9 values equally spaced in
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$\left[ 0, .28\right]$. We simulate 324 different collections for each
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value of $\eps[\pi]$ and $\eps[\rho]$.
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$\pi\rho\text{-}colBiSBM$, $\pi\text{-}colBiSBM$,
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$\rho\text{-}colBiSBM$, $iid\text{-}colBiSBM$ and
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$sep\text{-}BiSBM$ are put in competition and the model with the
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greater BIC-L is selected as the \emph{preferred model}.
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When $\eps[\pi] = 0$, $\bm{\pi}^1 = \bm{\pi}^2$, $\eps[\rho] = 0$
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and $\bm{\rho}^1 = \bm{\rho}^2$, the generated collection is an
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$iid\text{-}colBiSBM$. When $\eps[\pi] > 0$ or
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$\bm{\pi}^1 \neq \bm{\pi}^2$, the model is a $\pi\text{-}colBiSBM$.
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When $\eps[\rho] > 0$ or $\bm{\rho}^1 \neq \bm{\rho}^2$, the model
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is a $\rho\text{-}colBiSBM$. Finally, when $\eps[\pi] > 0$ or
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$\bm{\pi}^1 \neq \bm{\pi}^2$ and $\eps[\rho] > 0$ or
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$\bm{\rho}^1 \neq \bm{\rho}^2$, the model is a
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$\pi\rho\text{-}colBiSBM$.
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\begin{table}[!h]
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\caption{\label{tab:tables}\label{tab:pi-model-sel}Model selection for varying $\pi$ mixture parameters}
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\centering
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\begin{tabular}[t]{lccccl}
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\toprule
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\multicolumn{1}{c}{ } & \multicolumn{4}{c}{Models} & \multicolumn{1}{c}{Blocks} \\
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\cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6}
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$\eps[\pi]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_1$ \\
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\midrule
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0.00 & 0.65 & 0.00 & 0.35 & 0.00 & 3 \\
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0.04 & 0.66 & 0.00 & 0.34 & 0.00 & 3 \\
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0.07 & 0.64 & 0.01 & 0.34 & 0.01 & 3.01 $\pm$ 0.01 \\
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0.11 & 0.63 & 0.03 & 0.31 & 0.03 & 3.01 $\pm$ 0.01 \\
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0.14 & 0.55 & 0.12 & 0.28 & 0.05 & 3 \\
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\addlinespace
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0.18 & 0.39 & 0.26 & 0.21 & 0.13 & 3.01 \\
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0.21 & 0.23 & 0.42 & 0.13 & 0.23 & 3.01 \\
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0.25 & 0.10 & 0.56 & 0.05 & 0.29 & 3.02 $\pm$ 0.01 \\
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0.28 & 0.01 & 0.65 & 0.01 & 0.33 & 3.01 $\pm$ 0.01 \\
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\bottomrule
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\end{tabular}
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\end{table}
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\begin{table}[!h]
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\caption{\label{tab:tables}\label{tab:rho-model-sel}Model selection for varying $\rho$ mixture parameters}
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\centering
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\begin{tabular}[t]{lccccl}
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\toprule
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\multicolumn{1}{c}{ } & \multicolumn{4}{c}{Models} & \multicolumn{1}{c}{Blocks} \\
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\cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6}
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$\eps[\rho]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_2$ \\
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\midrule
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0.00 & 0.63 & 0.37 & 0.00 & 0.00 & 3 \\
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0.04 & 0.65 & 0.34 & 0.00 & 0.01 & 3 \\
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0.07 & 0.64 & 0.33 & 0.01 & 0.01 & 3 \\
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0.11 & 0.64 & 0.31 & 0.03 & 0.02 & 3 \\
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0.14 & 0.53 & 0.29 & 0.11 & 0.06 & 3 \\
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\addlinespace
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0.18 & 0.42 & 0.20 & 0.24 & 0.14 & 3.01 \\
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0.21 & 0.25 & 0.12 & 0.40 & 0.22 & 3.01 \\
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0.25 & 0.08 & 0.06 & 0.58 & 0.29 & 3.01 \\
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0.28 & 0.01 & 0.01 & 0.65 & 0.32 & 3 \\
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\bottomrule
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\end{tabular}
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\end{table}
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\begin{figure}[H]
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% \includegraphics{./Rcodes/simulation/img/plot_model_function_eps.png}
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\caption{Plot of preferred model in function of $\eps[\pi]$ and $\eps[\rho]$}
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\label{fig:pref_model_func_eps}
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\end{figure}
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\paragraph{Results:}
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On the figure \ref{fig:pref_model_func_eps} and tables
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\ref{tab:pi-model-sel} and \ref{tab:rho-model-sel}, one can see that
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there is a turning point around $\eps[\pi] = 0.2$ (resp.
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$\eps[\rho] = 0.2$), before which $iid\text{-}colBiSBM$ and
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$\rho\text{-}colBiSBM$ (resp. $\pi\text{-}colBiSBM$) are selected
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most of the times and after $0.2$ the $\pi\text{-}colBiSBM$ (resp.
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$\rho\text{-}colBiSBM$) and $\pi\rho\text{-}colBiSBM$ gets more and
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more selected, highlighting our capacity to recover the simulated
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structure.
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\paragraph*{Remark:}
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Please note that when ``Recovered $Q_1$(or $Q_2$)'' is not an
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integer it's because some procedures returned a value other than 3.
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Binary file not shown.
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@ -8,9 +8,13 @@
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\usepackage[cyr]{aeguill} % Police vectorielle TrueType, guillemets francais
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\usepackage{epsfig} % pour gérer les images
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\usepackage{amsmath,amsthm, mathtools} % très bon mode mathématique
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\usepackage{amsfonts,amssymb,bm, bbold}% permet la definition des ensembles
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\usepackage{amsfonts,amssymb,bm}% permet la definition des ensembles
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\DeclareMathAlphabet{\mathbbb}{U}{bbold}{m}{n} % Pour l'indicatrice
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\usepackage{algorithm2e} % pour les algorithmes
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\usepackage{algpseudocode} % pour les algorithmes
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% \usepackage{algpseudocode} % pour les algorithmes
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\RestyleAlgo{ruled}
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\usepackage{float} % pour le placement des figure
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\usepackage{url} % pour une gestion efficace des url
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\usepackage[citecolor=blueind,urlcolor=blueps,bookmarks=false,hypertexnames=true]{hyperref} % pour les hyperliens dans le document
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\usepackage[outline]{contour}
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\usepackage[super]{nth}
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\usepackage{caption} % Figures
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\usepackage{subcaption} % And Subfigures
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\usepackage{titling}
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\usepackage{rotating} % For allowing to rotate figures
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\usepackage{svg} % To allow svg inclusions
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\usepackage{float} % To allow Pandoc to control figure placement
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\floatplacement{figure}{H}
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\floatplacement{table}{H}
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\usepackage{booktabs} % For good tables
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% FancyHDR
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% Images
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\graphicspath{{../img/}{../figure/}}
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% Figure placement
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\floatplacement{figure}{t}
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%% Tikz Related
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\usetikzlibrary{calc,shapes,backgrounds,arrows,automata,shadows,positioning,
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arrows,shapes,positioning,shadows,trees,calc,backgrounds,
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automata,positioning}
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\tikzset{
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basic/.style = {draw, text width=3cm, font=\sffamily, rectangle},
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root/.style = {basic, rounded corners=2pt, thin, align=center,
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@ -203,15 +205,13 @@ automata,positioning}
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\pagenumbering{roman}
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\tableofcontents
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\include{remerciements}
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\include{chapter1-presentation_UMR}
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% \include{chapter1-presentation_UMR}
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\end{selectlanguage}
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\begin{selectlanguage}{english}
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\pagenumbering{arabic}
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\include{chapter2-context}
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\include{chapter3-structure-detection}
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\include{chapter4-simulation-studies}
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% \chapter{Applications}
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@ -221,8 +221,8 @@ automata,positioning}
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\addtocounter{maincontentend}{1}
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\addtocounter{customchapter}{1}
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\printbibliography
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\listoffigures
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\listoftables
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% \listoffigures
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% \listoftables
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\end{selectlanguage}
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\end{document}
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21
tables/simulations/inference/iid.tex
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21
tables/simulations/inference/iid.tex
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\begin{table}[!h]
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\caption{\label{tab:per_model_iid}Quality metrics for $iid$$\text{-}colBiSBM$}
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\centering
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\begin{tabular}[t]{rllllll}
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\toprule
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$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & $\mathbbb{1}_{\widehat{Q_1}=Q_1}$ & $\mathbbb{1}_{\widehat{Q_2}=Q_2}$\\
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\midrule
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0.00 & 0 & 0 & 0 & 0 & 0 & 0\\
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0.03 & 0.01 & 0.02 & 0.01 & 0.02 & 0 & 0\\
|
||||
0.06 & 0.7 $\pm$ 0.01 & 0.69 $\pm$ 0.01 & 0.55 $\pm$ 0.02 & 0.54 $\pm$ 0.02 & 0.61 $\pm$ 0.05 & 0.63 $\pm$ 0.05\\
|
||||
0.09 & 0.96 & 0.95 & 0.86 $\pm$ 0.02 & 0.85 $\pm$ 0.02 & 0.95 $\pm$ 0.02 & 0.96 $\pm$ 0.02\\
|
||||
0.12 & 0.99 & 0.99 & 0.9 $\pm$ 0.02 & 0.89 $\pm$ 0.02 & 0.95 $\pm$ 0.02 & 0.86 $\pm$ 0.03\\
|
||||
\addlinespace
|
||||
0.15 & 1 & 0.99 & 0.91 $\pm$ 0.02 & 0.91 $\pm$ 0.02 & 0.94 $\pm$ 0.02 & 0.88 $\pm$ 0.03\\
|
||||
0.18 & 1 & 1 & 0.95 $\pm$ 0.01 & 0.94 $\pm$ 0.02 & 0.93 $\pm$ 0.03 & 0.97 $\pm$ 0.02\\
|
||||
0.21 & 1 & 1 & 0.94 $\pm$ 0.02 & 0.94 $\pm$ 0.02 & 0.94 $\pm$ 0.02 & 0.94 $\pm$ 0.02\\
|
||||
0.24 & 1 & 1 & 0.93 $\pm$ 0.02 & 0.92 $\pm$ 0.02 & 0.91 $\pm$ 0.03 & 0.92 $\pm$ 0.03\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
21
tables/simulations/inference/pi.tex
Normal file
21
tables/simulations/inference/pi.tex
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
\begin{table}[!h]
|
||||
|
||||
\caption{\label{tab:per_model_pi}Quality metrics for $\pi$$\text{-}colBiSBM$}
|
||||
\centering
|
||||
\begin{tabular}[t]{rllllll}
|
||||
\toprule
|
||||
$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & $\mathbbb{1}_{\widehat{Q_1}=Q_1}$ & $\mathbbb{1}_{\widehat{Q_2}=Q_2}$\\
|
||||
\midrule
|
||||
0.00 & 0 & 0 & 0 & 0 & 0 & 0\\
|
||||
0.03 & 0.01 & 0.02 & 0.01 & 0.01 & 0 & 0\\
|
||||
0.06 & 0.74 $\pm$ 0.01 & 0.71 $\pm$ 0.01 & 0.62 $\pm$ 0.02 & 0.58 $\pm$ 0.02 & 0.59 $\pm$ 0.05 & 0.64 $\pm$ 0.05\\
|
||||
0.09 & 0.97 & 0.95 & 0.87 $\pm$ 0.02 & 0.84 $\pm$ 0.02 & 0.71 $\pm$ 0.04 & 1\\
|
||||
0.12 & 1 & 0.98 & 0.91 $\pm$ 0.02 & 0.89 $\pm$ 0.02 & 0.73 $\pm$ 0.04 & 1\\
|
||||
\addlinespace
|
||||
0.15 & 1 & 0.99 & 0.93 $\pm$ 0.02 & 0.91 $\pm$ 0.02 & 0.84 $\pm$ 0.04 & 1\\
|
||||
0.18 & 1 & 0.99 & 0.94 $\pm$ 0.01 & 0.92 $\pm$ 0.02 & 0.85 $\pm$ 0.03 & 1\\
|
||||
0.21 & 1 & 0.99 & 0.91 $\pm$ 0.02 & 0.87 $\pm$ 0.03 & 0.81 $\pm$ 0.04 & 1\\
|
||||
0.24 & 1 & 0.99 & 0.93 $\pm$ 0.02 & 0.9 $\pm$ 0.02 & 0.83 $\pm$ 0.04 & 0.99 $\pm$ 0.01\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
21
tables/simulations/inference/pirho.tex
Normal file
21
tables/simulations/inference/pirho.tex
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
\begin{table}[!h]
|
||||
|
||||
\caption{\label{tab:per_model_pirho}Quality metrics for $\pi\rho$$\text{-}colBiSBM$}
|
||||
\centering
|
||||
\begin{tabular}[t]{rllllll}
|
||||
\toprule
|
||||
$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & $\mathbbb{1}_{\widehat{Q_1}=Q_1}$ & $\mathbbb{1}_{\widehat{Q_2}=Q_2}$\\
|
||||
\midrule
|
||||
0.00 & 0 & 0 & 0 & 0 & 0 & 0\\
|
||||
0.03 & 0.01 & 0.01 & 0.01 & 0.02 & 0 & 0\\
|
||||
0.06 & 0.76 $\pm$ 0.01 & 0.75 $\pm$ 0.01 & 0.65 $\pm$ 0.02 & 0.64 $\pm$ 0.02 & 0.86 $\pm$ 0.03 & 0.83 $\pm$ 0.04\\
|
||||
0.09 & 0.97 & 0.97 & 0.91 $\pm$ 0.02 & 0.91 $\pm$ 0.02 & 0.9 $\pm$ 0.03 & 0.92 $\pm$ 0.03\\
|
||||
0.12 & 1 & 1 & 0.92 $\pm$ 0.02 & 0.91 $\pm$ 0.02 & 0.91 $\pm$ 0.03 & 0.86 $\pm$ 0.03\\
|
||||
\addlinespace
|
||||
0.15 & 1 & 1 & 0.95 $\pm$ 0.02 & 0.94 $\pm$ 0.02 & 0.93 $\pm$ 0.03 & 0.91 $\pm$ 0.03\\
|
||||
0.18 & 1 & 1 & 0.91 $\pm$ 0.02 & 0.91 $\pm$ 0.02 & 0.87 $\pm$ 0.03 & 0.86 $\pm$ 0.03\\
|
||||
0.21 & 1 & 1 & 0.94 $\pm$ 0.02 & 0.94 $\pm$ 0.02 & 0.91 $\pm$ 0.03 & 0.93 $\pm$ 0.03\\
|
||||
0.24 & 1 & 1 & 0.93 $\pm$ 0.02 & 0.93 $\pm$ 0.02 & 0.9 $\pm$ 0.03 & 0.91 $\pm$ 0.03\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
21
tables/simulations/inference/preferred.tex
Normal file
21
tables/simulations/inference/preferred.tex
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
\begin{table}[!h]
|
||||
|
||||
\caption{\label{tab:proportion-preferred-table}Proportions of models selected per \eps[\alpha] (data for Figure \ref{fig:inference-proportion-preferred})}
|
||||
\centering
|
||||
\begin{tabular}[t]{rccccc}
|
||||
\toprule
|
||||
\eps[\alpha] & $sep\text{-}BiSBM$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$\\
|
||||
\midrule
|
||||
0.00 & 1.00 & 0.00 & 0.00 & 0.00 & 0.00\\
|
||||
0.03 & 0.52 & 0.25 & 0.06 & 0.09 & 0.07\\
|
||||
0.06 & 0.01 & 0.04 & 0.13 & 0.06 & 0.77\\
|
||||
0.09 & 0.00 & 0.04 & 0.02 & 0.00 & 0.94\\
|
||||
0.12 & 0.00 & 0.04 & 0.00 & 0.00 & 0.96\\
|
||||
\addlinespace
|
||||
0.15 & 0.00 & 0.05 & 0.00 & 0.00 & 0.95\\
|
||||
0.18 & 0.00 & 0.06 & 0.00 & 0.00 & 0.94\\
|
||||
0.21 & 0.00 & 0.05 & 0.00 & 0.00 & 0.95\\
|
||||
0.24 & 0.00 & 0.03 & 0.00 & 0.00 & 0.97\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
21
tables/simulations/inference/rho.tex
Normal file
21
tables/simulations/inference/rho.tex
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
\begin{table}[!h]
|
||||
|
||||
\caption{\label{tab:per_model_rho}Quality metrics for $\rho$$\text{-}colBiSBM$}
|
||||
\centering
|
||||
\begin{tabular}[t]{rllllll}
|
||||
\toprule
|
||||
$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & $\mathbbb{1}_{\widehat{Q_1}=Q_1}$ & $\mathbbb{1}_{\widehat{Q_2}=Q_2}$\\
|
||||
\midrule
|
||||
0.00 & 0 & 0 & 0 & 0 & 0 & 0\\
|
||||
0.03 & 0.01 & 0.01 & 0.01 & 0.02 & 0 & 0\\
|
||||
0.06 & 0.72 $\pm$ 0.01 & 0.74 $\pm$ 0.01 & 0.57 $\pm$ 0.02 & 0.6 $\pm$ 0.02 & 0.61 $\pm$ 0.05 & 0.56 $\pm$ 0.05\\
|
||||
0.09 & 0.94 & 0.97 & 0.83 $\pm$ 0.02 & 0.85 $\pm$ 0.02 & 1 & 0.6 $\pm$ 0.05\\
|
||||
0.12 & 0.98 & 1 & 0.87 $\pm$ 0.02 & 0.9 $\pm$ 0.02 & 1 & 0.75 $\pm$ 0.04\\
|
||||
\addlinespace
|
||||
0.15 & 0.98 & 1 & 0.83 $\pm$ 0.03 & 0.88 $\pm$ 0.02 & 1 & 0.72 $\pm$ 0.04\\
|
||||
0.18 & 0.98 & 1 & 0.82 $\pm$ 0.03 & 0.87 $\pm$ 0.02 & 0.99 $\pm$ 0.01 & 0.71 $\pm$ 0.04\\
|
||||
0.21 & 0.98 & 1 & 0.87 $\pm$ 0.02 & 0.9 $\pm$ 0.02 & 1 & 0.77 $\pm$ 0.04\\
|
||||
0.24 & 0.98 & 1 & 0.84 $\pm$ 0.03 & 0.88 $\pm$ 0.02 & 1 & 0.72 $\pm$ 0.04\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
21
tables/simulations/inference/sep.tex
Normal file
21
tables/simulations/inference/sep.tex
Normal file
|
|
@ -0,0 +1,21 @@
|
|||
\begin{table}[!h]
|
||||
|
||||
\caption{\label{tab:per_model_sep}Quality metrics for $sep\text{-}BiSBM$}
|
||||
\centering
|
||||
\begin{tabular}[t]{rllll}
|
||||
\toprule
|
||||
$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$\\
|
||||
\midrule
|
||||
0.00 & 0 & 0 & 0 & 0\\
|
||||
0.03 & 0.01 & 0.02 & 0.02 & 0.02\\
|
||||
0.06 & 0.69 $\pm$ 0.02 & 0.68 $\pm$ 0.02 & 0.38 $\pm$ 0.02 & 0.36 $\pm$ 0.02\\
|
||||
0.09 & 0.97 & 0.96 & 0.55 $\pm$ 0.02 & 0.52 $\pm$ 0.02\\
|
||||
0.12 & 1 & 1 & 0.51 $\pm$ 0.02 & 0.52 $\pm$ 0.02\\
|
||||
\addlinespace
|
||||
0.15 & 1 & 1 & 0.54 $\pm$ 0.02 & 0.54 $\pm$ 0.02\\
|
||||
0.18 & 1 & 1 & 0.56 $\pm$ 0.02 & 0.54 $\pm$ 0.02\\
|
||||
0.21 & 1 & 1 & 0.56 $\pm$ 0.02 & 0.57 $\pm$ 0.02\\
|
||||
0.24 & 1 & 1 & 0.57 $\pm$ 0.02 & 0.57 $\pm$ 0.02\\
|
||||
\bottomrule
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
407
tikz/simulations/inference/model-proportions.tex
Normal file
407
tikz/simulations/inference/model-proportions.tex
Normal file
|
|
@ -0,0 +1,407 @@
|
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\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (137.83,235.14) rectangle (154.23,242.65);
|
||||
\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);
|
||||
\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);
|
||||
\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);
|
||||
\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);
|
||||
\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);
|
||||
\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);
|
||||
\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);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\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 ( 33.61,117.93) {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 ( 33.61,199.06) {0.75};
|
||||
|
||||
\node[text=drawColor,anchor=base east,inner sep=0pt, outer sep=0pt, scale= 0.88] at ( 33.61,239.62) {1.00};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\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] ( 35.81,120.96) --
|
||||
( 38.56,120.96);
|
||||
|
||||
\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] ( 35.81,202.09) --
|
||||
( 38.56,202.09);
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,line join=round] ( 35.81,242.65) --
|
||||
( 38.56,242.65);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\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] ( 73.10, 69.53) --
|
||||
( 73.10, 72.28);
|
||||
|
||||
\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] (109.57, 69.53) --
|
||||
(109.57, 72.28);
|
||||
|
||||
\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] (146.03, 69.53) --
|
||||
(146.03, 72.28);
|
||||
|
||||
\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] (182.49, 69.53) --
|
||||
(182.49, 72.28);
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,line join=round] (200.72, 69.53) --
|
||||
(200.72, 72.28);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\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 ( 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 ( 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 (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 (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 (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 (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 (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 (198.58, 48.63) {0.24};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\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) {$\epsilon_{\alpha}$};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,rotate= 90.00,anchor=base,inner sep=0pt, outer sep=0pt, scale= 1.10] at ( 13.08,161.52) {Preferred model proportions};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{RGB}{255,255,255}
|
||||
|
||||
\path[fill=fillColor] (228.04,106.34) rectangle (283.58,216.71);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.10] at (233.54,202.56) {Preferred};
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 1.10] at (233.54,190.68) {Model};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{gray}{0.92}
|
||||
|
||||
\path[fill=fillColor] (233.54,169.66) rectangle (247.99,184.11);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{230,159,0}
|
||||
\definecolor{fillColor}{RGB}{230,159,0}
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (234.25,170.37) rectangle (247.28,183.40);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{gray}{0.92}
|
||||
|
||||
\path[fill=fillColor] (233.54,155.20) rectangle (247.99,169.66);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{86,180,233}
|
||||
\definecolor{fillColor}{RGB}{86,180,233}
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (234.25,155.92) rectangle (247.28,168.95);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{gray}{0.92}
|
||||
|
||||
\path[fill=fillColor] (233.54,140.75) rectangle (247.99,155.20);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,158,115}
|
||||
\definecolor{fillColor}{RGB}{0,158,115}
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (234.25,141.46) rectangle (247.28,154.49);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{gray}{0.92}
|
||||
|
||||
\path[fill=fillColor] (233.54,126.30) rectangle (247.99,140.75);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{240,228,66}
|
||||
\definecolor{fillColor}{RGB}{240,228,66}
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (234.25,127.01) rectangle (247.28,140.04);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{fillColor}{gray}{0.92}
|
||||
|
||||
\path[fill=fillColor] (233.54,111.84) rectangle (247.99,126.30);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,114,178}
|
||||
\definecolor{fillColor}{RGB}{0,114,178}
|
||||
|
||||
\path[draw=drawColor,line width= 0.6pt,fill=fillColor] (234.25,112.55) rectangle (247.28,125.59);
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (253.49,173.86) {sep};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (253.49,159.40) {iid};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (253.49,144.95) {$\pi$};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (253.49,130.49) {$\rho$};
|
||||
\end{scope}
|
||||
\begin{scope}
|
||||
\path[clip] ( 0.00, 0.00) rectangle (289.08,289.08);
|
||||
\definecolor{drawColor}{RGB}{0,0,0}
|
||||
|
||||
\node[text=drawColor,anchor=base west,inner sep=0pt, outer sep=0pt, scale= 0.88] at (253.49,116.04) {$\pi\rho$};
|
||||
\end{scope}
|
||||
\end{tikzpicture}
|
||||
Loading…
Add table
Reference in a new issue