adding related works

1 files changed, 30 insertions, 2 deletions

diff --git a/finale/mid_report.tex b/finale/mid_report.tex
index e35a839..3a808d5 100644
--- a/finale/mid_report.tex
+++ b/finale/mid_report.tex
@@ -69,6 +69,35 @@ Two subquestions:
         faster (use a Bayesian prior)?
 \end{itemize}
 
+\subsection*{Related work}
+The study of edge prediction in graphs has been an active field of research for
+over a decade~\cite{Nowell08, Leskovec07, AdarA05}.~\cite{GomezRodriguez:2010}
+introduced the {\scshape Netinf} algorithm, which approximates the likelihood of
+cascades represented as a continuous process.  The algorithm was improved in
+later work~\cite{gomezbalduzzi:2011}, but is not known to have any theoretical
+guarantees beside empirical validation on synthetic networks.
+\cite{Netrapalli:2012} studied the discrete-time version of the independent
+cascade model and obtained the first ${\cal O}(s^2 \log m)$ recovery guarantee
+on general networks, by using unregularized MLE and making a {\it correlation
+decay\/} assumption, which limits the number of new infections at every step. In
+this setting, they show a lower bound of the number of cascades needed for
+support recovery with constant probability of the order $\Omega(s \log (m/s))$.
+They also suggest a {\scshape Greedy} algorithm, which achieves a ${\cal O}(s
+\log m)$ guarantee in the case of tree graphs. The work of~\cite{Abrahao:13}
+studies the same continuous-model framework as \cite{GomezRodriguez:2010} and
+obtains an ${\cal O}(s^9 \log^2 s \log m)$ support recovery algorithm, without
+the \emph{correlation decay} assumption.  \cite{du2013uncover,Daneshmand:2014}
+propose Lasso regularization of MLE for recovering the weights of the graph
+under a continuous-time independent cascade model. The work
+of~\cite{du2014influence} is slightly orthogonal to ours since they suggest
+learning the \emph{influence} function, rather than the parameters of the
+network directly.
+
+More recently, the inference of Hawkes process is perhaps the closest related
+topic to our work, with recent papers \cite{linderman2014discovering,
+linderman2015scalable} , focusing on MLE, EM, and Variational
+Inference methods to learning these processes.
+
 \section{Model}
 
 Weighted directed graph $G = (V, \Theta)$. $k=|V|$ is the number of nodes.
@@ -95,7 +124,6 @@ Markovian process:
 $\bt_i$ is the $i$th column of $\Theta$, $f:\R\to[0,1]$, plus independence for
 $i$. A cascade continues until no more infected nodes. 
 
-
 \section{Identifiability}
 
 A given source distribution $p_s$ and \cref{eq:markov} completely specifies the
@@ -329,6 +357,6 @@ given $(x_t)_{t\geq1}$}$ \Comment{Update posterior on $\theta$}
 \end{algorithm}
 
 \bibliography{sparse}{}
-\bibliographystyle{plain}
+\bibliographystyle{alpha}
 
 \end{document}