\addtocounter{customchapter}{1}
\chapter{Conclusions and future work}
\label{chap:conclusions-and-future-work}
\section{Conclusion}
\label{sec:conclusion}

\subsection{Difficulties encountered}
\paragraph{Seed dependance} While using our clustering on


\section{Future work}
\label{sec:future-work}

\paragraph{Identifiability}
As stated in section~\ref{sec:model-identifiability}, we only have
identifiability for the \emph{iid}-colBiSBM and we will work on establishing
identifiability for $\pi$, $\rho$ and $\pi\rho$ models.

\paragraph{Finding a trade-off between \emph{iid} and $\pi\rho$}
We observed while testing clustering with the different models that
the $\pi$, $\rho$ and $\pi\rho$ model, with their increased number of parameters
for block memberships parameters tends to give smaller BIC-L criterion values
while having a higher Evidence Lower Bound than the \emph{iid}.
This arises because of the penalties on the block memberships and support that
increase significantly and exceeds the gain on the ELBO and the diminution of
the connectivity parameters.
An idea to tackle this problem could be to suppose that the block memberships
for network $m$ are themselves the realizations of random variables and
thus introduce sort of a mixed effect model.

\paragraph{Comparison to other graphs clustering methods}
Recent work have been comparing
colSBM~\parencite{chabert-liddellLearningCommonStructures2024a} and
graphclust~\parencite{rebafkaModelbasedClusteringMultiple2023} assessing various
capabilities of the models and particularly focusing on networks clustering.
We will reproduce and adapt the analysis to test other simulation settings that
were not considered in this work.

\section*{Thank you for reading this work}