3.2

1 files changed, 4 insertions, 4 deletions

diff --git a/problem.tex b/problem.tex
index 2e4db20..c3c7c09 100644
--- a/problem.tex
+++ b/problem.tex
@@ -56,7 +56,7 @@ $D$-optimality criterion
 
 Note that the estimator $\hat{\beta}$ is a linear map of $y_S$; as $y_S$ is a multidimensional normal r.v., so is $\hat{\beta}$ (the randomness coming from the noise terms $\varepsilon_i$ and the prior on $\beta$). 
 In particular, $\hat{\beta}$ has 
-covariance $\sigma^2(R+\T{X_S}X_S)^{-1}$. As such, maximizing $I(\beta;y_S)$ can alternatively be seen as a means of reducing the uncertainty on estimator $\hat{\beta}$ my minimizing the product of the eigenvalues of its covariance.
+covariance $\sigma^2(R+\T{X_S}X_S)^{-1}$. As such, maximizing $I(\beta;y_S)$ can alternatively be seen as a means of reducing the uncertainty on estimator $\hat{\beta}$ by minimizing the product of the eigenvalues of its covariance.
 
 %An alternative interpretation, given that $(R+ \T{X_S}X_S)^{-1}$ is the covariance of the estimator $\hat{\beta}$, is that it tries to minimize the 
 %which is indeed a function of the covariance matrix $(R+\T{X_S}X_S)^{-1}$.
@@ -124,9 +124,9 @@ In particular, consider the greedy algorithm in which, for
  $S\subseteq\mathcal{N}$ the set constructed thus far, the next
 element $i$  included is the one which maximizes the
 \emph{marginal-value-per-cost}, \emph{i.e.},
-\begin{align}
-    i = \argmax_{j\in\mathcal{N}\setminus S}\frac{V(S\cup\{i\}) - V(S)}{c_i}\label{greedy}
-\end{align}
+%\begin{align}
+  $  i = \argmax_{j\in\mathcal{N}\setminus S}{(V(S\cup\{i\}) - V(S))}/{c_i}.$ %\label{greedy}
+%\end{align}
 This is repeated until adding an element in $S$ exceeds the budget
  $B$. Denote by $S_G$ the set constructed by this heuristic and let
 $i^*=\argmax_{i\in\mathcal{N}} V(\{i\})$ be the element of maximum singleton value. Then,