From 4110319283b3b5b667d215bd44f23f8cd1a7cf46 Mon Sep 17 00:00:00 2001
From: Jean Pouget-Abadie <jean.pougetabadie@gmail.com>
Date: Thu, 7 May 2015 21:25:36 -0400
Subject: broke something w/ references + changed RE paragraph

---
 paper/sections/model.tex | 15 ++++++---------
 1 file changed, 6 insertions(+), 9 deletions(-)

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

diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index b478e94..acec974 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -192,7 +192,7 @@ Generalized Linear Cascade model with inverse link function $f:z\mapsto
 1-e^{-\epsilon\cdot z}$.
 
 \subsubsection{Logistic Cascades}
-
+\label{sec:logistic_cascades}
 Consider the specific case of ``logistic cascades'' (where $f$ is the logistic
 function). This model captures the idea that there is a threshold around which
 each additional neighbor's contribution becomes significant: logistic
@@ -201,10 +201,7 @@ Threshold model~\cite{Kempe:03}. As we will see later in the
 analysis, the Hessian of our optimization program simplifies in the case of a
 logistic inverse link function to $\nabla^2\mathcal{L}(\theta^*) =
 \frac{1}{|\mathcal{T}|}XX^T$ where $X$ is the observation matrix $[x^1 \ldots
-x^\mathcal{|T|}]$. The (RE)-condition we introduce subsequently is then
-equivalent to the assumption made in the Lasso analysis of~\cite{bickel:2009}.
-
-
+x^\mathcal{|T|}]$.
 
 % \subsection{The Linear Threshold Model}
 
@@ -234,10 +231,10 @@ equivalent to the assumption made in the Lasso analysis of~\cite{bickel:2009}.
 
 \begin{figure}
   \includegraphics[scale=.4]{figures/drawing.pdf}
-  \caption{Illustration of the sparse-recovery approach: the measurement matrix
-  is known, as is a Bernoulli realization of the matrix-vector product via the
-non-linear transformation induced by $f$. Our objective is to recover the
-unknown weight vector $\theta_i$ for each node $i$.}
+  \caption{Illustration of the sparse-recovery approach. Our objective is to
+  recover the unknown weight vector $\theta_j$ for each node $j$. We observe a
+Bernoulli realization of the $f$ transform of the matrix-vector product, where
+the measurement matrix encodes which nodes are ``contagious''}
 \end{figure}
 
 
-- 
cgit v1.2.3-70-g09d2

