From 8a611d4cc0e979d62ee29a75d757bfd2b3ff0cdb Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 6 Feb 2015 16:25:28 -0500
Subject: Cosmetic changes

---
 paper/sections/results.tex | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

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

diff --git a/paper/sections/results.tex b/paper/sections/results.tex
index c39f9da..5d63cbd 100644
--- a/paper/sections/results.tex
+++ b/paper/sections/results.tex
@@ -130,9 +130,10 @@ $\hat{\theta}_\lambda$ is the solution of \eqref{eq:pre-mle}:
 
 To prove Theorem~\ref{thm:main}, we apply Lemma~\ref{lem:negahban} with
 $\tau_{\mathcal{L}}=0$. Since $\mathcal{L}$ is twice differentiable and convex,
-assumption \eqref{eq:rc} is implied by the restricted eigenvalue condition
-\eqref{eq:re}. The upper bound on the $\ell_{\infty}$ norm of
-$\nabla\mathcal{L}(\theta^*)$ is given by Lemma~\ref{lem:ub}.
+assumption \eqref{eq:rc} with $\kappa_{\mathcal{L}}=\frac{\gamma}{2}$ is
+implied by the (RE) condition \eqref{eq:re}. The upper bound
+on the $\ell_{\infty}$ norm of $\nabla\mathcal{L}(\theta^*)$ is given by
+Lemma~\ref{lem:ub}.
 
 \begin{lemma}
 \label{lem:ub}
@@ -335,7 +336,8 @@ We will need the following additional assumptions on the inverse link function $
     \left|\frac{f''}{f}\right|\right)
     \leq\frac{1}{\alpha}
 \end{equation}
-whenever $f(\inprod{\theta^*}{x})\notin\{0,1\}$.
+whenever $f(\inprod{\theta^*}{x})\notin\{0,1\}$. These conditions are once
+again non restrictive in the (IC) model and (V) model.
 
 \begin{proposition}
     \label{prop:fi}
@@ -391,8 +393,7 @@ m)$.
 \paragraph{(RE) vs Irrepresentability Condition}
 
 \cite{Daneshmand:2014} rely on an `incoherence' condition on the hessian of the
-likelihood function. Their condition is equivalent to the more commonly called
-{\it (S,s)-irrepresentability} condition:
+likelihood function also known as the {\it (S,s)-irrepresentability} condition:
 
 \begin{comment}
 \begin{definition}
-- 
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