related

1 files changed, 5 insertions, 7 deletions

diff --git a/general.tex b/general.tex
index 429299a..5f80c58 100644
--- a/general.tex
+++ b/general.tex
@@ -29,9 +29,9 @@ where $\mu$ is the smallest eigenvalue of $R$.
 \subsection{Non-Bayesian Setting}
 
 In the non-bayesian setting, \emph{i.e.} when the experimenter has no prior
-distribution on the model, the covariance matrix $R$ is the zero matrix and
-ridge regression \eqref{ridge} reduces to simple least squares. In this case,
-the $D$-optimal criterion takes the following form:
+distribution on the model, the covariance matrix $R$ is the zero matrix. In this case,
+the ridge regression estimation proceedure \eqref{ridge} reduces to simple least squares (\emph{i.e.}, linear regression),
+and the $D$-optimality reduces to the entropy of $\hat{\beta}$, given by:
 \begin{equation}\label{eq:d-optimal}
 V(S) = \log\det(X_S^TX_S)
 \end{equation}
@@ -46,16 +46,14 @@ and individual rationality.
 \begin{lemma}
 For any $M>1$, there is no $M$-approximate, truthful, budget feasible,
 individually rational mechanism for a budget feasible reverse auction with
-value function $V(S) = \det{\T{X_S}X_S}$.  For any $M>1$, there is no
-$M$-approximate, truthful, budget feasible, individually rational mechanism for
-a budget feasible reverse auction with $V(S) =  \det{\T{X_S}X_S}$.
+value function $V(S) = \det{\T{X_S}X_S}$.  
 \end{lemma}
 
 \begin{proof}
 \input{proof_of_lower_bound1}
 \end{proof}
 
-Beyond $D$-optimality, several other objectives such as $E$-optimality (maximizing the smallest eigenvalue of $\T{X_S}X_S$) or $T$-optimality (maximizing $\mathrm{trace}(\T{X_S}{X_S}))$ are encountered in the literature \cite{pukelsheim2006optimal}, though they do not relate to entropy as $D$-optimality. We leave the task of approaching the maximization of such objectives from a strategic point of view as an open problem.
+%Beyond $D$-optimality, several other objectives such as $E$-optimality (maximizing the smallest eigenvalue of $\T{X_S}X_S$) or $T$-optimality (maximizing $\mathrm{trace}(\T{X_S}{X_S}))$ are encountered in the literature \cite{pukelsheim2006optimal}, though they do not relate to entropy as $D$-optimality. We leave the task of approaching the maximization of such objectives from a strategic point of view as an open problem.
 
 \subsection{Beyond Linear Models}
 Selecting experiments that maximize the information gain in the Bayesian setup