Add subset selection application

1 files changed, 9 insertions, 0 deletions

diff --git a/results.tex b/results.tex
index 8e6a186..ce5368d 100644
--- a/results.tex
+++ b/results.tex
@@ -209,6 +209,15 @@ sets are the sets of size at most one).
         This can be written as multivariate concave over modular
         (\textbf{TODO:} I think multivariate concave over modular is not
         submodular in general, it is for $\log\det$. Understand this better).
+    \item \emph{data subset selection/summarization:} in statistical machine
+        translation, Bilmes used sum of concave over modular:
+        \begin{displaymath}
+            f(S) = \sum_{f} \lambda_f \phi\left(\sum_{e\in S}w_f(e)\right)
+        \end{displaymath}
+        where each $f$ represents a feature, $w_f(e)$ represents how much of
+        $f$ element $e$ has, and $\phi$ captures decreasing marginal gain when
+        we have a lot of a given feature.
+        Facility location functions are also commonly used for subset selection.
 \end{itemize}
 
 \section{Passive Optimization}