general

1 files changed, 4 insertions, 4 deletions

diff --git a/problem.tex b/problem.tex
index 5631f7a..363731a 100644
--- a/problem.tex
+++ b/problem.tex
@@ -121,12 +121,12 @@ Each experiment $i\in
 private. In order to obtain the measurement $y_i$, the experimenter  needs to
 pay agent $i$ a price that exceeds her cost. 
 
-For example, each $i$ may correspond to a human participant; the
+For example, each $i$ may correspond to a human subject; the
 feature vector $x_i$ may correspond to a normalized vector of her age, weight,
 gender, income, \emph{etc.}, and the measurement $y_i$ may capture some
 biometric information (\emph{e.g.}, her red cell blood count, a genetic marker,
-etc.). The cost $c_i$ is the amount the participant deems sufficient to
-incentivize her participation in the study. Note that, in this setup, the feature vectors $x_i$ are public information that the experimenter can consult prior the experiment design. Moreover, though a participant may lie about her true cost $c_i$, she cannot lie about $x_i$ (\emph{i.e.}, all features are verifiable upon collection) or $y_i$ (\emph{i.e.}, she cannot falsify her measurement).
+etc.). The cost $c_i$ is the amount the subject deems sufficient to
+incentivize her participation in the study. Note that, in this setup, the feature vectors $x_i$ are public information that the experimenter can consult prior the experiment design. Moreover, though a subject may lie about her true cost $c_i$, she cannot lie about $x_i$ (\emph{i.e.}, all features are verifiable upon collection) or $y_i$ (\emph{i.e.}, she cannot falsify her measurement).
 
 %\subsection{D-Optimality Criterion}
 Ideally, motivated by the $D$-optimality criterion, we would like to design a mechanism that maximizes \eqref{dcrit} within a good approximation ratio. As \eqref{dcrit} may take arbitrarily small negative values, to define a meaningful approximation one would consider  the (equivalent) maximization of $V(S) = \det\T{X_S}X_S$. %, for some strictly increasing, on-to function $f:\reals_+\to\reals_+$. 
@@ -170,7 +170,7 @@ Though a variety of different measures of information exist in literature (see,
 \end{align} 
 %where $H(\beta)$ is the entropy of the prior distribution and $\entropy(\beta \mid E)$ is the conditional entropy con
 \subsection{Linear Regression}
-In this paper, we focus on \emph{linear regression} experiments, aiming to discover a linear function from user data. In particular, we consider a set of $n$ users $\mathcal{N} = \{1,\ldots, n\}$. Each user
+In this paper, we focus on \emph{linear regression} experiments, aiming to discover a linear function from data. In particular, we consider a set of $n$ users $\mathcal{N} = \{1,\ldots, n\}$. Each user
 $i\in\mathcal{N}$ has a public vector of features $x_i\in\reals^d$, $\norm{x_i}_2\leq 1$, and an
 undisclosed piece of information $y_i\in\reals$. 
 For example, the features could be the age, weight, or height of user $i$, while the latter can be her propensity to contract a disease.