rapport : NA echange AUC et ARI pour cohérence + début interp

rapport/chapter4-simulations/na-robustness.tex

@@ -61,24 +61,46 @@ and we store the same predictions.
 \emph{Area Under the Curve} (AUC) for predicted versus real link values and the
 ARI for predicted versus real block memberships.
 
-\begin{figure}[ht]
+\begin{figure}[H]
-    \centering
-    \includestandalone{tikz/simulations/na_robustness/auc-model}
-    \caption{}
-    \label{fig:auc-plot}
-\end{figure}
-
-\begin{figure}[ht]
     \centering
     \includestandalone{tikz/simulations/na_robustness/ari-dim-model}
-    \caption{}
+    \caption{ARI in function of $p_\texttt{NA}$, the proportion of missing links
+        for various colBiSBM models and their LBM counterparts}
     \label{fig:ari-dim-plot-na}
 \end{figure}
 
+\begin{figure}[H]
+    \centering
+    \includestandalone{tikz/simulations/na_robustness/auc-model}
+    \caption{AUC in function of $p_\texttt{NA}$, the proportion of missing links
+        for various colBiSBM models and their LBM counterparts}
+    \label{fig:auc-plot}
+\end{figure}
 
 \paragraph{Results}
 Figures~\ref{fig:auc-plot} and~\ref{fig:ari-dim-plot-na} show a
-box plot named \enquote{sep-$model$} that
+box plots named \enquote{sep-$model$} that
 corresponds to the results given by a LBM fitted on data generated with the
-corresponding \emph{model}. These sep box plots are there to serve as a baseline
+corresponding \emph{model}. We will compare the results for one model box plot
-to compare model by model.
+to the corresponding sep-model box plot, serving as a baseline.
+
+% TODO the ARI interpretation
+For the figure~\ref{fig:ari-dim-plot-na},  in almost all cases
+
+For the figure~\ref{fig:auc-plot}, overall we observe results similar to
+the ARIs, namely  our models tend to have a slightly better AUC than their
+corresponding LBM.
+This indicates that link prediction benefits from the collection model
+in almost all cases.
+We may even be able to improve the results by using larger collections.
+
+For the cases where our models do not perform better, we observe that
+$\pi\rho$-colBiSBM in
+the modular case seems to do slightly worse than its LBM counterpart for the
+first values of $p_{\texttt{NA}}$. The $\rho$-colBiSBM seem to suffer from the
+same problem, and encounters it too for some values with the nested structure.
+This may have to do with our simulation parameters giving for this models
+cases that are harder.
+Or this may be due to mis-attribution of the block memberships resulting in
+wrong predictions.
+

tikz/simulations/na_robustness/auc-model.tex

@@ -1,4 +1,4 @@
-% Created by tikzDevice version 0.12.6 on 2024-07-24 16:25:30
+% Created by tikzDevice version 0.12.6 on 2024-07-24 17:05:02
 % !TEX encoding = UTF-8 Unicode
 \documentclass[10pt]{standalone}\usepackage{tikz}