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Miss_Figg on
Is the sum individual informativeness of two independent variables no more than their joint informativeness? ·
2019-07-08T15:39:36.282Z ·
LW ·
GW
We want to prove:
This can be rewritten as:
After moving everything to the right hand side and simplifying, we get:
Now if we just prove that is a probability distribution, then the left hand side is , and Kullback-Leibler divergence is always nonnegative.
Ok, q is obviously nonnegative, and its integral equals 1:
Q.e.d.