adding some references for ERGMs

2 files changed, 60 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}
 
 
diff --git a/finale/sparse.bib b/finale/sparse.bib
index 9fc56df..d2487c1 100644
--- a/finale/sparse.bib
+++ b/finale/sparse.bib
@@ -517,3 +517,47 @@ year = "2009"
         journal={arXiv preprint arXiv:1402.0914},
           year={2014}
 }
+
+
+@article{caimo2011bayesian,
+        title={Bayesian inference for exponential random graph models},
+        author={Caimo, Alberto and Friel, Nial}, journal={Social Networks},
+        volume={33},
+        number={1},
+        pages={41--55},
+        year={2011},
+        publisher={Elsevier}
+}
+
+@article{koskinen2010analysing,
+    title={Analysing exponential random graph (p-star) models with missing data
+      using Bayesian data augmentation},
+    author={Koskinen, Johan H and Robins, Garry L and Pattison, Philippa E},
+    journal={Statistical Methodology},
+    volume={7},
+    number={3},
+    pages={366--384},
+    year={2010},
+    publisher={Elsevier}
+}
+
+@article{robins2007recent,
+    title={Recent developments in exponential random graph (p*) models for
+      social networks},
+    author={Robins, Garry and Snijders, Tom and Wang, Peng and Handcock, Mark
+      and Pattison, Philippa},
+    journal={Social networks},
+    volume={29},
+    number={2},
+    pages={192--215},
+    year={2007},
+    publisher={Elsevier}
+}
+
+
+@article{simma2012modeling,
+    title={Modeling events with cascades of Poisson processes},
+    author={Simma, Aleksandr and Jordan, Michael I},
+    journal={arXiv preprint arXiv:1203.3516},
+    year={2012}
+}