From 3d818b2861faf0ccdbcb2eeb6ac90a07f4e4374a Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Mon, 18 May 2015 16:15:36 +0200
Subject: Pass on results section

---
 paper/sections/results.tex | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

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

diff --git a/paper/sections/results.tex b/paper/sections/results.tex
index 7eb3973..7fca661 100644
--- a/paper/sections/results.tex
+++ b/paper/sections/results.tex
@@ -43,8 +43,9 @@ by~\cite{bickel2009simultaneous}.
 A discussion of the $(S,\gamma)$-{\bf(RE)} assumption in the context of
 generalized linear cascade models can be found in Section~\ref{sec:re}. In our
 setting we require that the {\bf(RE)}-condition holds for the Hessian of the
-log-likelihood function $\mathcal{L}$: it essentially captures the fact that the
-binary vectors of the set of active nodes are not \emph{too} collinear.
+log-likelihood function $\mathcal{L}$: it essentially captures the fact that
+the binary vectors of the set of active nodes (\emph{i.e} the measurement) are
+not \emph{too} collinear.
 
 {\color{red} Rewrite the minimal assumptions necessary}
 We will also need the following assumption on the inverse link function $f$ of
@@ -318,7 +319,7 @@ again non restrictive in the (IC) model and (V) model.
 
 Observe that the number of measurements required in Proposition~\ref{prop:fi}
 is now quadratic in $s$. If we only keep the first measurement from each
-cascade which are independent, we can apply Theorem 1.8 from
+cascade, which are independent, we can apply Theorem 1.8 from
 \cite{rudelson:13}, lowering the number of required cascades to $s\log m \log^3(
 s\log m)$.
 
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