%We initiate the study of mechanisms for \emph{experimental design}. 

In the classical {\em experimental design} setting,
an  experimenter  \E\ with  a budget $B$ has access to a population of $n$ potential experiment subjects $i\in \{1,\ldots,n\}$,  each associated with a vector of features $x_i\in\reals^d$ as well as a cost $c_i>0$.
Conducting an experiment with subject $i$  reveals an unknown value $y_i\in \reals$ to \E. \E\ typically assumes some 
hypothetical relationship between  $x_i$'s and $y_i$'s, \emph{e.g.},  $y_i \approx  \T{\beta} x_i$, and estimates 
$\beta$ from experiments. 
%conducting the experiments and obtaining the measurements $y_i$ allows 
%\E\ can estimate  $\beta$. 
\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 mechanisms for experimental design. In this setting, 
subjects are \emph{strategic} and may lie about their costs. In particular, we formulate the {\em Experimental Design Problem} (\EDP) as finding a set $S$ of subjects that maximize $V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i})$ under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to  the information gain in  $\beta$ when it is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. We present the first known 
deterministic, polynomial time, truthful, budget feasible mechanism for \EDP{}.
Our mechanism yields a constant factor ($\approx 19.68$) approximation, and we show that no truthful, budget-feasible algorithms are possible within a factor 2 approximation.
Our approach here generally applies to a wider class of learning problems and 
obtains polynomial time universally truthful (\emph{i.e.}, randomized) budget feasible mechanism, also within a constant factor approximation.



