From 13f312ce5b1201b70375d7cffebc813b25cb35fa Mon Sep 17 00:00:00 2001
From: Jean Pouget-Abadie <jean.pougetabadie@gmail.com>
Date: Thu, 30 Apr 2015 11:40:17 -0400
Subject: added more comments from reviewers

---
 paper/sections/model.tex | 11 ++++++++---
 1 file changed, 8 insertions(+), 3 deletions(-)

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

diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index 19d7506..fbcedf3 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -25,7 +25,8 @@ contagious nodes ``influence'' other nodes in the graph to become contagious. An
 the successive states of the nodes in graph ${\cal G}$. Note that both the
 ``single source'' assumption made in~\cite{Daneshmand:2014} and
 \cite{Abrahao:13} as well as the ``uniformly chosen source set'' assumption made
-in~\cite{Netrapalli:2012} verify condition 3.
+in~\cite{Netrapalli:2012} verify condition 3. {\color{red} why is it less
+restrictive? explain}
 
 In the context of Graph Inference,~\cite{Netrapalli:2012} focus
 on the well-known discrete-time independent cascade model recalled below, which
@@ -103,7 +104,7 @@ In the independent cascade model, nodes can be either susceptible, contagious
 or immune. At $t=0$, all source nodes are ``contagious'' and all remaining
 nodes are ``susceptible''. At each time step $t$, for each edge $(i,j)$ where
 $j$ is susceptible and $i$ is contagious, $i$ attempts to infect $j$ with
-probability $p_{i,j}\in]0,1]$; the infection attempts are mutually independent.
+probability $p_{i,j}\in(0,1]$; the infection attempts are mutually independent.
 If $i$ succeeds, $j$ will become contagious at time step $t+1$. Regardless of
 $i$'s success, node $i$ will be immune at time $t+1$. In other words, nodes
 stay contagious for only one time step. The cascade process terminates when no
@@ -147,6 +148,9 @@ step $t$, then we have:
 Thus, the linear voter model is a Generalized Linear Cascade model
 with inverse link function $f: z \mapsto z$.
 
+{\color{red} \subsubsection{Discretization of Continous Model}
+TODO}
+
 % \subsection{The Linear Threshold Model}
 
 % In the Linear Threshold Model, each node $j\in V$ has a threshold $t_j$ from
@@ -171,6 +175,7 @@ with inverse link function $f: z \mapsto z$.
 % X^t\right] = \text{sign} \left(\inprod{\theta_j}{X^t} - t_j \right)
 % \end{equation} where ``sign'' is the function $\mathbbm{1}_{\cdot > 0}$.
 
+{\color{red} Add drawing of math problem as in Edo's presentation}
 
 
 \subsection{Maximum Likelihood Estimation}
@@ -227,4 +232,4 @@ 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.
 
-{\color{red} TODO: talk about the different constraints}
+{\color{red} TODO:~talk about the different constraints}
-- 
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