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Lucas Fidon edited subsection_MI_based_metric_According__.tex
almost 8 years ago
Commit id: d643bbcee2e033c9120430231607009b6ae140f6
deletions | additions
diff --git a/subsection_MI_based_metric_According__.tex b/subsection_MI_based_metric_According__.tex
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...
\[d_{MI}(X,Y) = 1 - \frac{2MI(X,Y)}{S(X) + S(Y)} \]
Where $X$ and $Y$ are the positions of the two players.
This quantity may be interpreted as to the proportion of uncertainty that is not shared between $X$ and $Y$.
Indeed it comes from the previous section that:
\begin{enumerate}
\item $d_{MI}$ is symmetric.
...
\item $d_{MI}(X,Y) = 0$ iff $X$ and $Y$ have the same probability law.
\item in particular $d_{MI}(X,X) = 0$ for any trajectory.
\item $d_{MI}(X,Y) = 1$ iff $X$ and $Y$ are independent.
\end{enumerate}
This quantity may be interpreted as to the proportion of uncertainty that is not shared between $X$ and $Y$.