From 16cee067526887f62dc725612d7f34730fddb447 Mon Sep 17 00:00:00 2001
From: Jean Pouget-Abadie <jean.pougetabadie@gmail.com>
Date: Thu, 7 May 2015 16:28:52 -0400
Subject: added references and reworded stuff

---
 paper/sections/abstract.tex | 19 ++++++++++---------
 1 file changed, 10 insertions(+), 9 deletions(-)

(limited to 'paper/sections/abstract.tex')

diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex
index 72a9bf4..3b28765 100644
--- a/paper/sections/abstract.tex
+++ b/paper/sections/abstract.tex
@@ -1,11 +1,12 @@
-In the Graph Inference problem, one seeks to recover the edges of an unknown
-graph from the observations of cascades propagating over this graph.
-In this paper, we approach this problem from the sparse recovery perspective.
-We introduce a general model of cascades, including the voter model and the independent cascade model, for which we provide the first algorithm which recovers the graph's edges with high
-probability and ${\cal O}(s\log m)$ measurements where
-$s$ is the maximum degree of the graph and $m$ is the number of nodes.
-Furthermore, we show that our algorithm also recovers the edge weights (the
-parameters of the diffusion process) and is robust in the context of
-approximate sparsity. Finally we prove an almost matching lower bound of
+In the Network Inference problem, one seeks to recover the edges of an unknown
+graph from the observations of cascades propagating over this graph.  In this
+paper, we approach this problem from the sparse recovery perspective.  We
+introduce a general model of cascades, including the voter model and the
+independent cascade model, for which we provide the first algorithm which
+recovers the graph's edges with high probability and ${\cal O}(s\log m)$
+measurements where $s$ is the maximum degree of the graph and $m$ is the number
+of nodes.  Furthermore, we show that our algorithm also recovers the edge
+weights (the parameters of the diffusion process) and is robust in the context
+of approximate sparsity. Finally we prove an almost matching lower bound of
 $\Omega(s\log\frac{m}{s})$ and validate our approach empirically on synthetic
 graphs.
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