From ac70a17ecab6c0efb26166c953b2f14fba2d2b87 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Tue, 8 Dec 2015 16:38:24 -0500
Subject: Final report template

---
 finale/sections/related.tex | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 finale/sections/related.tex

(limited to 'finale/sections/related.tex')

diff --git a/finale/sections/related.tex b/finale/sections/related.tex
new file mode 100644
index 0000000..59fb759
--- /dev/null
+++ b/finale/sections/related.tex
@@ -0,0 +1,41 @@
+\paragraph{Related works.}
+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, relying on
+Maximum-Likelihood and convex relaxations was improved in later
+work~\cite{gomezbalduzzi:2011}, but is not known to have any theoretical
+guarantees beside empirical validation on synthetic networks.
+
+Let us denote by $m$ the number of nodes in the graph and for a given node, we
+denote by $s$ its in-degree. In what follows, we call a \emph{recovery
+guarantee} an upper bound on the number of observations required (expressed as
+a function of $s$ and $m$) to learn the incoming edges of a node to a fixed
+arbitrary accuracy level. \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.  They also suggest a {\scshape Greedy} algorithm,
+with provably good performance in tree graphs, which maintains a counter of
+each node's antecedents, i.e. the set of nodes infected at a prior time step to
+its infection time. 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 continuous process studied in previous work has been
+reformulated as a Hawkes process, with recent papers
+\cite{linderman2014discovering, linderman2015scalable, simma2012modeling},
+focusing on Expectation-Maximization, and Variational Inference methods to learn
+these processes. Because of the discrete nature of the GLC model, we hope to
+bring a better understanding to the link between the properties of a graph and
+its \emph{learnability}. We wish to further explore the idea of non-product
+priors raised in \cite{linderman2014discovering, linderman2015scalable}, since
+the experimental validation of their work focused on simple graph priors.
+Finally, the \emph{Active Learning} formulation is, to the best of the
+authors' knowledge, novel in this context.
-- 
cgit v1.2.3-70-g09d2

