From 99ce9bed50afa1b1f8b11e97d40f8642e6fed865 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Mon, 18 May 2015 19:27:59 +0200
Subject: fixed typos

---
 paper/sections/model.tex | 15 +++++++--------
 1 file changed, 7 insertions(+), 8 deletions(-)

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

diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index 26e1a8d..8d403e1 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -137,7 +137,7 @@ with inverse link function $f : z \mapsto 1 - e^{-z}$.
 Note that to write the Independent Cascade Model as a Generalized Linear
 Cascade Model, we had to introduce the change of variable $\Theta_{i,j}
 = \log(\frac{1}{1-p_{i,j}})$. The recovery results in Section~\ref{sec:results}
-hold on the $\Theta_j$ parameters. Fortunately, the following lemma shows that
+pertain to the $\Theta_j$ parameters. Fortunately, the following lemma shows that
 the recovery error on $\Theta_j$ is an upper bound on the error on the original
 $p_j$ parameters.
 
@@ -178,7 +178,7 @@ independent cascade model with exponential transmission function (CICE)
 of~\cite{GomezRodriguez:2010, Abrahao:13, Daneshmand:2014}. Assume that the
 temporal resolution of the discretization is $\varepsilon$, \emph{i.e.} all
 nodes whose (continuous) infection time is within the interval $[k\varepsilon,
-    (k+1)\varepsilon)$ are considered infected at (discrete) time step $t$. Let
+    (k+1)\varepsilon)$ are considered infected at (discrete) time step $k$. Let
     $X^k$ be the indicator vector of the set of nodes `infected' before or
     during the $k^{th}$ time interval.  Note that contrary to the discrete-time
     independent cascade model, $X^k_j = 1 \implies X^{k+1}_j = 1$, that is,
@@ -292,13 +292,12 @@ measurements and not the number of cascades.
 
 \paragraph{Regularity assumptions}
 
-We would like program~\eqref{eq:pre-mle} to be a convex program in order to
+We would like program~\eqref{eq:pre-mle} to be convex in order to
 solve it efficiently. A sufficient condition is to
-assume that $\mathcal{L}_i$ is a concave function. This will be the case if,
-for example, $f$ and $(1-f)$ are both log-concave functions. Remember that
-a twice-differentiable function $f$ is log-concave iff. $f''f \leq f'^2$. It is
-easy to verify this property for $f$ and $(1-f)$ in the Independent Cascade
-Model and Voter Model.
+assume that $\mathcal{L}_i$ is a concave function, which is the case if $f$ and
+$(1-f)$ are both log-concave functions. Remember that a twice-differentiable
+function $f$ is log-concave iff. $f''f \leq f'^2$. It is easy to verify this
+property for $f$ and $(1-f)$ in the Independent Cascade Model and Voter Model.
 
 Furthermore, the data-dependent bounds in Section~\ref{sec:main_theorem} will
 require the following regularity assumption on the inverse link function $f$:
-- 
cgit v1.2.3-70-g09d2

