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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} |