muthu intro

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@@ -15,16 +15,16 @@ In our setup, experiments cannot be manipulated and hence measurements are consi
 is a cost $c_i$ associated with experimenting on
 subject $i$ which varies from subject to subject. This may be viewed as the  
 cost subject $i$ incurs when tested, and hence $i$ needs to be reimbursed; or, it might be viewed as the incentive for $i$
-to participate in the experiment; or, it might be the inherent value of the data.  When subjects are strategic, they may have an incentive to mis-report their cost. This economic aspect has always been inherent in experimental design: experimenters often work within strict budgets and design creative incentives. However, we are not aware of principled study of this setting from a strategic point of view. 
+to participate in the experiment; or, it might be the inherent value of the data.  This economic aspect has always been inherent in experimental design: experimenters often work within strict budgets and design creative incentives. However, we are not aware of principled study of this setting from a strategic point of view. When subjects are strategic, they may have an incentive to mis-report their cost. 
 
 
 Our contributions are as follows.
 \begin{itemize}
 \item
-We formulate the problem of experimental design subject to a given budget, in presence of strategic agents who specify their costs. In particular, we focus on linear regression. This is naturally viewed  as a budget feasible mechanism design problem with a sophisticated objective function that is related to the covariance of the $x_i$'s. In particular we formulate the  {\em Experimental Design Problem} (\EDP) as follows: the experimenter \E\ wishes to maximize 
+We formulate the problem of experimental design subject to a given budget, in presence of strategic agents who specify their costs. In particular, we focus on linear regression. This is naturally viewed  as a budget feasible mechanism design problem. We show that  the objective function is sophisticated and related to the covariance of the $x_i$'s. In particular we formulate the  {\em Experimental Design Problem} (\EDP) as follows: the experimenter \E\ wishes to find set $S$ of subjects to maximize 
 \begin{align}V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) \label{obj}\end{align}
-subject to the budget constraint $\sum_{i\in S}c_i\leq B$, where $B$ is \E's budget. %, and other {\em strategic constraints} we don't list here.
- The objective function, which is the key, is motivated from the so-called $D$-objective criterion; in particular, it captures the reduction in the entropy of $\beta$ when the latter is learned  through regression methods.
+with a  budget constraint $\sum_{i\in S}c_i\leq B$, where $B$ is \E's budget. %, and other {\em strategic constraints} we don't list here.
+ The objective function, which is the key, is motivated from the so-called $D$-objective criterion; in particular, it captures the reduction in the entropy of $\beta$ when the latter is learned  through linear regression methods.
 
 \item
 The above objective is submodular.