From 705f11ce5e6cf6dbd41e8a055743d711b8f8fbdb Mon Sep 17 00:00:00 2001 From: Thibaut Horel Date: Mon, 5 Nov 2012 16:27:15 +0100 Subject: More fixes, reapply some lost changes overwritten by previous merge --- intro.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'intro.tex') diff --git a/intro.tex b/intro.tex index 2e5c8af..2156be5 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. 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 -- cgit v1.2.3-70-g09d2