From fca9d9fca8141e104b792ce0b27346d83af71b82 Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Mon, 11 Feb 2013 19:29:32 -0800
Subject: small changes

---
 abstract.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'abstract.tex')

diff --git a/abstract.tex b/abstract.tex
index a92ad45..9e00a95 100644
--- a/abstract.tex
+++ b/abstract.tex
@@ -10,15 +10,15 @@ hypothetical relationship between  $x_i$'s and $y_i$'s, \emph{e.g.},  $y_i \appr
 $\beta$ from experiments. 
 %conducting the experiments and obtaining the measurements $y_i$ allows 
 %\E\ can estimate  $\beta$. 
-As a proxy for various practical constraints, \E{} may select subjects to select for the experiments. 
+As a proxy for various practical constraints, \E{} may select only a subset of subjects on which to conduct the experiment. 
 %\E 's  goal is to select which experiments to conduct, subject to her budget constraint.
 %, to obtain the best estimate possible for $\beta$.
 
 We initiate the study of budgeted mechanisms for experimental design. In this setting,  \E{} has a budget $B$.  
 Each subject $i$ declares associated cost $c_i >0$ to be part of the experiment, and must be paid at least their cost.  Further,  the subjects 
-are \emph{strategic} and may lie about their costs . In particular, we formulate the {\em Strategic Experimental Design Problem} (\SEDP) as finding a set $S$ of subjects for the experiment that maximizes $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to  the information gain in  parameter  $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. 
+are \emph{strategic} and may lie about their costs. In particular, we formulate the {\em  Experimental Design Problem} (\SEDP) as finding a set $S$ of subjects for the experiment that maximizes $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to  the information gain in  parameter  $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. 
 
 We present a deterministic, polynomial time, truthful, budget feasible mechanism for \SEDP{}.
-By applying previous work on budget feasible mechanisms with submodular objective, one could have derived either an exponential time deterministic mechanism or a randomized  polynomial time mechanism. Our mechanism yields a constant factor ($\approx 12.68$) approximation, and we show that no truthful, budget-feasible algorithms are possible within a factor $2$ approximation.  We also show how to apply our approach to a wide class of learning problems. 
+By applying previous work on budget feasible mechanisms with submodular objective, one could have derived either an exponential time deterministic mechanism or a randomized  polynomial time mechanism. Our mechanism yields a constant factor ($\approx 12.68$) approximation, and we show that no truthful, budget-feasible algorithms are possible within a factor $2$ approximation.  We also show how to genralize our approach to a wide class of learning problems. 
 
 
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