From 85d2de4ff3588b8059b2bb45ec9444097b996aa7 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 6 Feb 2015 18:27:55 -0500
Subject: Typos

---
 paper/sections/intro.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

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

diff --git a/paper/sections/intro.tex b/paper/sections/intro.tex
index d52da66..39f5089 100644
--- a/paper/sections/intro.tex
+++ b/paper/sections/intro.tex
@@ -46,7 +46,7 @@ The contributions of this paper are the following:
     \item we formulate the Graph Inference problem in the context of
         discrete-time influence cascades as a sparse recovery problem for
         a specific type of Generalized Linear Model. This formulation notably
-        encompases the well-studied Independent Cascade Model and Voter Model.
+        encompasses the well-studied Independent Cascade Model and Voter Model.
     \item we give an algorithm which recovers the graph's edges using $\O(s\log
         m)$ cascades. Furthermore, we show that our algorithm is also able to
         recover the edge weights (the parameters of the influence model),
@@ -55,7 +55,7 @@ The contributions of this paper are the following:
         recover is approximately $s$-sparse by proving guarantees in the
         \emph{stable recovery} setting.
     \item we provide an almost tight lower bound of $\Omega(s\log \frac{m}{s})$
-        observations.
+        observations required for sparse recovery.
 \end{itemize}
 
 The organization of the paper is as follows: we conclude the introduction by
@@ -69,7 +69,7 @@ Section~\ref{sec:experiments}.
 \paragraph{Related Work}
 
 The study of edge prediction in graphs has been an active field of research for
-over a decade \cite{Nowell08} \cite{Leskovec07} \cite{AdarA05}.
+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
@@ -82,7 +82,7 @@ analysis depends on 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 an ${\cal O}(s \log m)$ guarantee in the case
+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.
@@ -99,7 +99,7 @@ m)$, by exploiting similar properties of the convex program's KKT conditions.
 In contrast, our work studies discrete-time diffusion processes including the
 Independent Cascade model under weaker assumptions. Furthermore, we analyze
 both the recovery of the graph's edges and the estimation of the model's
-parameters, and achieve closer to optimal bounds.
+parameters, and achieve close to optimal bounds.
 
 \begin{comment}
 Their work has the merit of studying a generalization of the discrete-time independent cascade model to continuous functions. Similarly to \cite{Abrahao:13}, they place themselves in
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