From b0d1e82017eb270398a5747ff2b46969e720b52a Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Mon, 5 Nov 2012 13:13:54 -0800
Subject: intro abstract muthu

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 abstract.tex | 21 +++++++++++++++++----
 1 file changed, 17 insertions(+), 4 deletions(-)

(limited to 'abstract.tex')

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-We initiate the study of mechanisms for \emph{experimental design}. In this setting,
-an  experimenter 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 the experimenter. Assuming a linear relationship between $x_i$'s and $y_i$'s, \emph{i.e.},  $y_i \approx  \T{\beta} x_i$, conducting the experiments and obtaining the measurements $y_i$ allows the experimenter to estimate  $\beta$. The experimenter's goal is to select which experiments to conduct, subject to her budget constraint, to obtain the best estimate possible. 
+%We initiate the study of mechanisms for \emph{experimental design}. 
 
-We study this problem when 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 mechanism for \EDP{}, yielding a constant factor ($\approx 19.68$) approximation, and show that no truthful algorithms are possible within a factor 2 approximation. Moreover, we show that a wider class of learning problems admits a polynomial time universally truthful (\emph{i.e.}, randomized) mechanism, also within a constant factor approximation.
+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 assume 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.
 
 
 
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