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I have a table that looks like this

  --Predicted --------------------
      Blue    | 0.15 | 0.25  | 0.4  
      Green   | 0.15 | 0.475 | 0.2  
      Red     | 0.7  | 0.275 | 0.4 
              | Red  | Green | Blue 
              ----  Actual --------

The sum of each column is equal to one. They are actually the conditional probabilities, for example the probability to predict a red when the actual was red is 70%. Similarly, the probability to predict a blue when the actual one was green was 25%, etc...

How do I calculate the mutual information for this table please? I dont think that is possible with only these numbers above, i need the counts in each cell I believe, is that right? For example, how are you going to calc the prob that a ball has a real/actual color of red? Thanks!

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If you only have the conditional probabilities $p(x|y)$ where $x$ is the predicted and $y$ the actual, you will also need the probability $p(y)$ of the actual. This way you can compute $p(x, y) = p(x|y) \cdot p(y)$ and from that you can get the MI.

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