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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 |