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Lucas Fidon added subsubsection_Mutual_Information_There_are__.tex
almost 8 years ago
Commit id: 707788c24d312bcd85bbf7e51c1482b3085597df
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\subsubsection{Mutual Information}
There are several equivalent ways to define Mutual Information.
The most intuitive definition is the following:
Let $X : P_1 \rightarrow E_1$ and $Y: P_2 \rightarrow E_2$ be two random variables, where $E_1$ and $E_2$ are two discrete probability spaces.
We define the Mutual information of$ X$ and $Y$, noted $I(X,Y)$ as:$
\[I(X,Y) = \sum{x \in E_1, y \in E_2}P_{(X,Y)}(x,y)*log(\frac{log(P_{(X,Y)}(x,y))}{P_{X}(x)P_{Y}(y)})\]
