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@@ -24,7 +24,7 @@ Our contributions are as follows. 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} 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. + 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. \item The above objective is submodular. |