From c29302b25adf190f98019eb8ce5f79b10b66d54d Mon Sep 17 00:00:00 2001 From: Thibaut Horel Date: Mon, 5 Nov 2012 16:04:20 +0100 Subject: Typos --- intro.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'intro.tex') diff --git a/intro.tex b/intro.tex index 54b5c11..8c3c5d7 100644 --- a/intro.tex +++ b/intro.tex @@ -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. -- cgit v1.2.3-70-g09d2