39 lines
No EOL
1.7 KiB
TeX
39 lines
No EOL
1.7 KiB
TeX
\addtocounter{customchapter}{1}
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\chapter{Conclusions and future work}
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\label{chap:conclusions-and-future-work}
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\section{Conclusion}
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\label{sec:conclusion}
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\subsection{Difficulties encountered}
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\paragraph{Seed dependance} While using our clustering on
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\section{Future work}
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\label{sec:future-work}
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\paragraph{Identifiability}
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As stated in section~\ref{sec:model-identifiability}, we only have
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identifiability for the \emph{iid}-colBiSBM and we will work on establishing
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identifiability for $\pi$, $\rho$ and $\pi\rho$ models.
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\paragraph{Finding a trade-off between \emph{iid} and $\pi\rho$}
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We observed while testing clustering with the different models that
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the $\pi$, $\rho$ and $\pi\rho$ model, with their increased number of parameters
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for block memberships parameters tends to give smaller BIC-L criterion values
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while having a higher Evidence Lower Bound than the \emph{iid}.
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This arises because of the penalties on the block memberships and support that
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increase significantly and exceeds the gain on the ELBO and the diminution of
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the connectivity parameters.
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An idea to tackle this problem could be to suppose that the block memberships
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for network $m$ are themselves the realizations of random variables and
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thus introduce sort of a mixed effect model.
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\paragraph{Comparison to other graphs clustering methods}
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Recent work have been comparing
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colSBM~\parencite{chabert-liddellLearningCommonStructures2024a} and
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graphclust~\parencite{rebafkaModelbasedClusteringMultiple2023} assessing various
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capabilities of the models and particularly focusing on networks clustering.
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We will reproduce and adapt the analysis to test other simulation settings that
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were not considered in this work.
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\section*{Thank you for reading this work} |