diff options
Diffstat (limited to 'intro.tex')
| -rw-r--r-- | intro.tex | 5 |
1 files changed, 5 insertions, 0 deletions
@@ -24,8 +24,13 @@ 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. 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. +<<<<<<< HEAD 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. +======= + 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. + +>>>>>>> c29302b25adf190f98019eb8ce5f79b10b66d54d \item The above objective is submodular. There are several recent results in budget feasible |