Timeline for Z-transforming Pearson correlation vs. converting to mutual information: they seem to be related, but how?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2021 at 17:33 | history | edited | Ariel | CC BY-SA 4.0 |
adding more intuition
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| Jun 6, 2021 at 14:24 | comment | added | Ariel | I think perhaps you misunderstood my answer. I was trying to make the case that these two measures are complimentary in that they are essentially measuring different aspects of the mutual dependence of the two random variables. As I pointed out in the answer, complete correlation, $\rho=\pm 1$ sends $I\to\infty$. Again, you should also read this answer which explains some more of the intuition behind the two quantities. | |
| Jun 6, 2021 at 13:59 | comment | added | Antichain | Thanks for you comment - it's nice to see how these are derived. Are there any specific connections between them (maybe some kind of transformation that turns one into the other, or an intuitive relationship between them?) They can be re-arranged as: $Z = -\frac{1}{2}(\ln(1-\rho) - \ln(1+\rho))$ $I =-\frac{1}{2}(\ln(1-\rho) + \ln(1+\rho))$ This seems too similar to be just a coincidence. | |
| Jun 6, 2021 at 3:21 | history | answered | Ariel | CC BY-SA 4.0 |