muthu

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 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. The objective function is sophisticated and 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 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}
 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.
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 The objective function, which is the key,  is obtained by optimizing  the information gain in  $\beta$ when it is learned  through linear regression methods, and is the so-called $D$-objective criterion in the literature. 
  
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+ The objective function, which is the key, is motivated from the so-called $D$-optimality criterion; in particular, it captures the reduction in the entropy of $\beta$ when the latter is learned  through linear regression methods.
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 \item
 The above objective is submodular. 
 There are several recent results in budget feasible