more rewriting of 3.3

1 files changed, 8 insertions, 1 deletions

diff --git a/paper/sections/results.tex b/paper/sections/results.tex
index c9f267a..8eda03f 100644
--- a/paper/sections/results.tex
+++ b/paper/sections/results.tex
@@ -257,7 +257,7 @@ irrepresentability condition considered in \cite{Daneshmand:2014}.
 \paragraph{Interpretation}
 
 There exists a large class of sufficient conditions under which sparse recovery
-is achievable in the context of regularized estimation. A good survey on these
+is achievable in the context of regularized estimation. A good survey on these
 different assumptions can be found in \cite{vandegeer:2009}.
 
 The restricted eigenvalue condition introduce in \cite{bickel:2009} is one of
@@ -286,6 +286,13 @@ case to the assumption made in the Lasso analysis of \cite{bickel:2009}.
 
 \paragraph{(RE) with high probability}
 
+The Generalized Linear Cascade model yields a probability distribution over the
+set observed nodes $x^t$. It is then natural to ask whether the restricted
+eigenvalue condition is likely to occur under this probabilistic model. Several
+recent papers show that large classes of correlated designs obey the restricted
+eigenvalue property with high probability \cite{raskutti:10}
+\cite{rudelson:13}. 
+
 Expressing the minimum restricted eigenvalue $\gamma$ as a function of the
 cascade model parameters is highly non-trivial. Yet, the restricted eigenvalue
 property is however well behaved in the following sense: under reasonable