rapport : simulations, inference ajout interprétation résultats

rapport/chapter4-simulations/inference.tex

@@ -116,14 +116,21 @@ and~\ref{fig:inference-ari-plots}.
 
 \paragraph{Results}
 For the model comparison, when $\eps[\alpha]$ is small
-($\eps[\alpha]\in[0, .04]$), the simulation model is close to the
-Erd\H{o}s-Reńyi network, and it is very hard to find any structure beyond the one
+($\eps[\alpha]\in[0, .03]$), the simulation model is close to an
+Erd\H{o}s-Reńyi network~\parencite{erdosRandomGraphs1959}, and it is very hard
+to find any structure beyond the one
 of a single block on each dimension.
 
-On the figure \ref{fig:inference-prop-modele-pref} one can see that from
-$\eps[\alpha] = 0.06$ around $70\%$ of the time the
+On the figure~\ref{fig:inference-prop-modele-pref} one can see that from
+$\eps[\alpha] = 0.06$ around $75\%$ of the time the
 $\pi\rho$-colBiSBM model (i.e., the correct one) is selected.
 
+The figure~\ref{fig:inference-ari-plots} shows that for $\eps[\alpha] \geq 0.09$,
+all the models, even the sep, have a
+$\overline{\text{ARI}}$ around $0.94$. This indicates that the models are able to
+assign correct nodes group memberships and thus that the inference works
+correctly.
+
 An interesting result we can read in the tables is that our models outperform
 the $sep\text{-}BiSBM$ when considering the ARI on the whole set of nodes
 ($\text{ARI}_d$). This means that our models are able to recover the block