From de7df38121cc8a39ee72899c9ed0628421dab7e1 Mon Sep 17 00:00:00 2001
From: jeanpouget-abadie <jean.pougetabadie@gmail.com>
Date: Wed, 28 Jan 2015 22:27:09 -0500
Subject: updated results section

---
 paper/sections/assumptions.tex | 7 +++++++
 1 file changed, 7 insertions(+)

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

diff --git a/paper/sections/assumptions.tex b/paper/sections/assumptions.tex
index eccd095..d6fed83 100644
--- a/paper/sections/assumptions.tex
+++ b/paper/sections/assumptions.tex
@@ -4,3 +4,10 @@ Proving the restricted eigenvalue assumption for correlated measurements is non-
 
 \subsection{The Irrepresentability Condition}
 
+If our objective is to recover only the support of the graph and to do it exactly , then the irrepresentability condition\footnote{{\it incoherence} in the text} used in \cite{Daneshmand:2014} is believed to be necessary. 
+
+However, assuming we only wish to recover all edges above a certain threshold, bounding the $\ell2$-error allows us to recover the full graph above a certain minimum threshold. Furthermore, it is intuitive that the irrepresentability condition is stronger than our suggested {\bf(RE)} assumption. In fact, by adapting slightly the following result from \cite{vandegeer:2009}, we can show that a `strong' irrepresentability condition directly {\it implies} the {\bf(RE)} condition for $\ell2$-recovery
+
+\begin{proposition}
+If the irrepresentability condition holds with $\epsilon > \frac{2}{3}$, then the restricted eigenvalue condition holds with constant: $(1 - 3\epsilon)^2 \lambda_{\min}n/s$
+\end{proposition}
\ No newline at end of file
-- 
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