From 282349d87a75e930bb4d2ac7bc389106d0519f0b Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Tue, 19 May 2015 00:00:17 +0200
Subject: Beginning of the compression

---
 paper/sections/model.tex | 8 ++------
 1 file changed, 2 insertions(+), 6 deletions(-)

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

diff --git a/paper/sections/model.tex b/paper/sections/model.tex
index fd25c27..532ee5e 100644
--- a/paper/sections/model.tex
+++ b/paper/sections/model.tex
@@ -140,13 +140,9 @@ the recovery error on $\Theta_j$ is an upper bound on the error on the original
 $p_j$ parameters.
 
 \begin{lemma}
+    \label{lem:transform}
     $\|\hat{\theta} - \theta^* \|_2 \geq \|\hat{p} - p^*\|_2$.
 \end{lemma}
-\begin{proof}
-Using the inequality $\forall x>0, \; \log x \geq 1 - \frac{1}{x}$, we have
-$|\log (\frac{1}{1 - p}) - \log (\frac{1}{1-p'})| \geq \max(1 - \frac{1-p}{1-p'},
-1 - \frac{1-p'}{1-p}) \geq \max( p-p', p'-p)$.
-\end{proof}
 
 \subsubsection{The Linear Voter Model}
 
@@ -334,7 +330,7 @@ $\mathcal{L}_i$ is equal to $-\infty$ when the parameters are outside of the
 domain of definition of the models, these contraints do not need to appear
 explicitly in the optimization program.
 
-In the specific case of the voter model the constraint $\sum_j \Theta_{i,j}
+In the specific case of the voter model, the constraint $\sum_j \Theta_{i,j}
 = 1$ will not necessarily be verified by the estimator obtained in
 \eqref{eq:pre-mle}. In some applications, the experimenter might not need this
 constraint to be verified, in which case the results in
-- 
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