From 0ff14f56819acfc7be77f9237e18417d465b2266 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Fri, 6 Feb 2015 15:48:24 -0500
Subject: Compression

---
 paper/sections/discussion.tex | 13 ++++---------
 1 file changed, 4 insertions(+), 9 deletions(-)

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

diff --git a/paper/sections/discussion.tex b/paper/sections/discussion.tex
index 9d7f491..10aa50b 100644
--- a/paper/sections/discussion.tex
+++ b/paper/sections/discussion.tex
@@ -1,6 +1,3 @@
-
-
-\paragraph{Future Work}
 Solving the Graph Inference problem with sparse recovery techniques opens new
 venues for future work. Firstly, the sparse recovery literature has already
 studied regularization patterns beyond the $\ell_1$-norm, notably the
@@ -12,16 +9,14 @@ has been obtained for the Lasso in the recent series of papers
 Finally, the linear threshold model is a commonly studied diffusion process and can also be cast as a \emph{generalized linear cascade} with inverse link function $z \mapsto \mathbbm{1}_{z > 0}$:
 $
     \label{eq:lt}
-    \tag{LT}
     X^{t+1}_j = \text{sign} \left(\inprod{\theta_j}{X^t} - t_j \right)
-    $
-
-This model therefore falls into the 1-bit compressed sensing model
-\cite{Boufounos:2008} framework. Several recent papers study the theoretical
+    $.
+This model therefore falls into the 1-bit compressed sensing framework
+\cite{Boufounos:2008}. Several recent papers study the theoretical
 guarantees obtained for 1-bit compressed sensing with specific measurements
 \cite{Gupta:2010, Plan:2014}. Whilst they obtained bounds of the order
 ${\cal O}(n \log \frac{n}{s}$), no current theory exists for recovering
-positive bounded signals from bernoulli hyperplanes. This research direction
+positive bounded signals from biniary measurememts. This research direction
 may provide the first clues to solve the ``adaptive learning'' problem: if we
 are allowed to adaptively \emph{choose} the source nodes at the beginning of
 each cascade, how much can we improve the current results?
-- 
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