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authorThibaut Horel <thibaut.horel@gmail.com>2012-11-05 02:18:05 +0100
committerThibaut Horel <thibaut.horel@gmail.com>2012-11-05 02:18:31 +0100
commit2a4664283998d5bf9c6615d251fd62c30001b73e (patch)
tree1554852eba4f43f1c6bc356d1df665ba6cd066f3 /general.tex
parent86b8f967a12fe5870fe7c8d0f765149c003832c6 (diff)
downloadrecommendation-2a4664283998d5bf9c6615d251fd62c30001b73e.tar.gz
Fix missing references
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@@ -79,13 +79,13 @@ The value function given by the information gain \eqref{general} is submodular.
\end{lemma}
\begin{proof}
-The theorem is proved in a slightly different context in \cite{guestrin}; we
+The theorem is proved in a slightly different context in \cite{krause2005near}; we
repeat the proof here for the sake of completeness. Using the chain rule for
the conditional entropy we get:
-\begin{displaymath}\label{eq:chain-rule}
+\begin{equation}\label{eq:chain-rule}
V(S) = H(y_S) - H(y_S \mid \beta)
= H(y_S) - \sum_{i\in S} H(y_i \mid \beta)
-\end{displaymath}
+\end{equation}
where the second equality comes from the independence of the $y_i$'s
conditioned on $\beta$. Recall that the joint entropy of a set of random
variables is a submodular function. Thus, our value function is written in