1 files changed, 16 insertions, 4 deletions
diff --git a/finale/mid_report.tex b/finale/mid_report.tex
index 3a808d5..38d9020 100644
--- a/finale/mid_report.tex
+++ b/finale/mid_report.tex
@@ -272,19 +272,31 @@ priors. We can:
 \item Take into account common graph structures, such as triangles, clustering
 \end{itemize}
 
-A common prior for graph is the ERGM model~\cite{}, defined by feature vector
-$s(G)$ and by the probability distribution:
+A common prior for graph is the Exponential Random Graph Model (ERGM), which
+allows flexible representations of networks and Bayesian inference. The
+distribution of an ERGM family is defined by feature vector $s(G)$ and by the
+probability distribution:
 $$P(G | \Theta) \propto \exp \left( s(G)\cdot \Theta \right)$$
 
+Though straightforward MCMC could be applied here, recent
+work~\cite{caimo2011bayesian, koskinen2010analysing, robins2007recent} has shown
+that ERGM inference has slow convergence and lack of robustness, developping
+better alternatives to naive MCMC formulations. Experiments using such a prior
+are ongoing, but we present only simple product distribution-type priors here.
+
 \paragraph{Inference}
 We can sample from the posterior by MCMC\@. This might not be the fastest
 solution however. We could greatly benefit from using an alternative method:
 \begin{itemize}
-\item EM\@. This approach was used in \cite{linderman2014discovering} to learn
+\item EM\@. This approach was used in \cite{linderman2014discovering,
+simma2012modeling} to learn
 the parameters of a Hawkes process, a closely related inference problem.
 \item Variational Inference. This approach was used
 in~\cite{linderman2015scalable} as an extension to the paper cited in the
-previous bullet point.
+previous bullet point. Considering the scalabilty of their approach, we hope to
+apply their method to our problem here, due to the similarity of the two
+processes, and to the computational constraints of running MCMC over a large
+parameter space.
 \end{itemize}