Timeline for Mutual information inequality
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 9, 2019 at 5:10 | vote | accept | Cesare | ||
| Aug 8, 2019 at 19:40 | comment | added | Steve | That's just convention, but I thought a different symbol for marginals and joint distribution might be easier to read. | |
| Aug 8, 2019 at 12:16 | comment | added | Cesare | Why did you have to introduce the $p_1$ and $p_2$ notation? | |
| Aug 8, 2019 at 10:33 | history | edited | Steve | CC BY-SA 4.0 |
edited body
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| Aug 8, 2019 at 9:02 | comment | added | Steve | Well, for negative $a$, the curve $a \mapsto I^a(X;Y)$ is increasing, so the highest value is at $a=0$, which shows the reverse of inequality (2). | |
| Aug 8, 2019 at 8:57 | comment | added | Cesare | Btw, your proof using the derivative is brilliant! | |
| Aug 8, 2019 at 8:56 | comment | added | Cesare | Yes, that is exactly what I mean. You seem to show that for negative $a$ the (pseudo) MI would increase. So that would imply that inequality 2 holds. Am I missing something? (sorry I deleted the previous comment cause I wanted to edit it and you were faster at replying). | |
| Aug 8, 2019 at 8:53 | comment | added | Steve | Not sure about a condition for $I^a(X;Y) \geq 0$. Could you make your counterexample more concrete? I might have gotten the terms confused with $I^{-a}$, I basically calculated with $I^a$ but also allowed $a \leq 0$. Of course, there might also be an error in my calculations. | |
| Aug 8, 2019 at 8:35 | history | answered | Steve | CC BY-SA 4.0 |