From 7df4228e025d5810cb1689073d42b6d8d265b018 Mon Sep 17 00:00:00 2001 From: jeanpouget-abadie Date: Sat, 31 Jan 2015 16:13:27 -0500 Subject: remodeling results section --- paper/sections/assumptions.tex | 2 ++ 1 file changed, 2 insertions(+) (limited to 'paper/sections/assumptions.tex') diff --git a/paper/sections/assumptions.tex b/paper/sections/assumptions.tex index 58ea977..5e412a4 100644 --- a/paper/sections/assumptions.tex +++ b/paper/sections/assumptions.tex @@ -1,3 +1,5 @@ +%There have been a series of papers arguing that the standard Lasso is an inappropriate exact variable selection method \cite{Zou:2006}, \cite{vandegeer:2011}, since it relies on the essentially necessary irrepresentability condition, introduced in \cite{Zhao:2006}. This is the condition on which the analysis of \cite{Daneshmand:2014} relies. It has been noted this condition is rather stringent and rarely holds in practical situations where correlation between variables occurs. Several alternatives have been suggested, including the adaptive and thresholded lasso, which relax this assumption. We defer an extended analysis of the irrepresentability assumption to Section~\ref{sec:assumptions}. + In this section, we compare the main assumption of \cite{Daneshmand:2014}, commonly known as the {\it irrepresentability condition}, to the restricted eigenvalue condition. We argue that the restricted eigenvalue is more likely to hold in practical situations. \subsection{The Irrepresentability Condition} -- cgit v1.2.3-70-g09d2