From 825d56f2f4e53eb162270fe4b3fa002f8b87a9fc Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Mon, 8 Jul 2013 22:25:21 +0200
Subject: Fix micro bug

---
 problem.tex | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

(limited to 'problem.tex')

diff --git a/problem.tex b/problem.tex
index 15f0c11..c21135b 100644
--- a/problem.tex
+++ b/problem.tex
@@ -3,7 +3,10 @@
 
 The theory of experimental design \cite{pukelsheim2006optimal,atkinson2007optimum,chaloner1995bayesian} considers the following formal setting. %  studies how an experimenter \E\  should select the parameters of a set of experiments she is about to conduct. In general, the optimality of a particular design depends on the purpose of the experiment, \emph{i.e.}, the quantity \E\  is trying to learn or the hypothesis she is trying to validate. Due to their ubiquity in statistical analysis, a large literature on the subject focuses on learning \emph{linear models}, where \E\ wishes to  fit  a linear function to the data she has collected.
 %Putting cost considerations aside
-Suppose that an experimenter \E\ wishes to conduct $k$ among $n$ possible experiments. Each experiment $i\in\mathcal{N}\defeq \{1,\ldots,n\}$ is associated with a set of parameters (or features) $x_i\in \reals^d$, normalized so that $$b\leq \|x_i\|_2\leq 1,$$ for some $b>0$. Denote by $S\subseteq \mathcal{N}$, where $|S|=k$, the set of experiments selected; upon its execution, experiment $i\in S$ reveals an output variable (the ``measurement'') $y_i$,  related to the experiment features $x_i$ through a linear function, \emph{i.e.},
+Suppose that an experimenter \E\ wishes to conduct $k$ among $n$ possible
+experiments. Each experiment $i\in\mathcal{N}\defeq \{1,\ldots,n\}$ is
+associated with a set of parameters (or features) $x_i\in \reals^d$, normalized
+so that $$b\leq \|x_i\|^2_2\leq 1,$$ for some $b>0$. Denote by $S\subseteq \mathcal{N}$, where $|S|=k$, the set of experiments selected; upon its execution, experiment $i\in S$ reveals an output variable (the ``measurement'') $y_i$,  related to the experiment features $x_i$ through a linear function, \emph{i.e.},
 \begin{align}\label{model}
      \forall i\in\mathcal{N},\quad y_i = \T{\beta} x_i + \varepsilon_i
 \end{align}
-- 
cgit v1.2.3-70-g09d2

