From ca4d1e1ae5038ab392d35d6815ff4f5f49fb188c Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Sun, 22 Sep 2013 17:08:04 -0400
Subject: Comment acks out and reduce conclusion

---
 conclusion.tex | 15 ++++++++++-----
 1 file changed, 10 insertions(+), 5 deletions(-)

(limited to 'conclusion.tex')

diff --git a/conclusion.tex b/conclusion.tex
index 6a3917e..94d8202 100755
--- a/conclusion.tex
+++ b/conclusion.tex
@@ -1,6 +1,11 @@
-We have proposed a convex relaxation for \EDP, and showed that it can be used to design a $\delta$-truthful, constant approximation mechanism that runs in polynomial time. Our objective function, commonly known as the Bayes $D$-optimality criterion, is motivated by linear regression, and in particular captures the information gain when experiments are used to learn a linear model. %in \reals^d.
+We have proposed a convex relaxation for \EDP, and showed that it can be used
+to design a $\delta$-truthful, constant approximation mechanism that runs in
+polynomial time. Our objective function, commonly known as the Bayes
+$D$-optimality criterion, is motivated by linear regression.
+%and in particular captures the information gain when experiments are used to learn a linear model in \reals^d.
 
-A natural question to ask is to what extent the results we present here
+A natural question to ask is to what extent the results
+%we present here
 generalize to other machine learning tasks beyond linear regression. We outline
 a path in pursuing such generalizations in Appendix~\ref{sec:ext}. In
 particular, although the information gain is not generally a submodular
@@ -9,15 +14,15 @@ outcomes are perturbed by independent noise, the information gain indeed
 exhibits submodularity. Several important  learning tasks fall under this
 category, including generalized linear regression, logistic regression,
 \emph{etc.} In light of this, it would be interesting to investigate whether
-our convex relaxation approach generalizes to other learning tasks in this
-broader class.
+our convex relaxation approach generalizes to other tasks in this broader class.
 
 The literature on experimental design includes several other optimality
 criteria~\cite{pukelsheim2006optimal,atkinson2007optimum}. Our convex
 relaxation \eqref{eq:our-relaxation} involved swapping the $\log\det$
 scalarization with the expectation appearing in the multi-linear extension
 \eqref{eq:multi-linear}. The same swap is known to yield concave objectives for
-several other optimality criteria, even when the latter are not submodular
+several other optimality criteria
+%, even when the latter are not submodular
 (see, \emph{e.g.}, \citeN{boyd2004convex}). Exploiting the convexity of such
 relaxations to design budget feasible mechanisms is an additional open problem
 of interest.
-- 
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