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| author | Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)> | 2012-11-05 09:40:54 -0800 |
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| committer | Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)> | 2012-11-05 09:40:54 -0800 |
| commit | 38152e6f14d7c5f91cee3c07e0ff2a00ef7b5a33 (patch) | |
| tree | 37373f53f9be005546346489f0383a36fff6b817 /intro.tex | |
| parent | c0400b1dcc65ea1018ff77f467721fc7d0ae9e4f (diff) | |
| parent | d4d9933432e1f15f9839d0e0ca14ff0f8656b814 (diff) | |
| download | recommendation-38152e6f14d7c5f91cee3c07e0ff2a00ef7b5a33.tar.gz | |
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| -rw-r--r-- | intro.tex | 2 |
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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. 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. -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 obtained by optimizing the information gain in $\beta$ when it is learned through linear regression methods, and is the so-called $D$-optimality criterion in the literature. \item The above objective is submodular. There are several recent results in budget feasible |
