Timeline for Regarding a new divergence function of two probability distributions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 2, 2015 at 21:11 | comment | added | Jeff | You are right that this function works in opposite of "divergence". Actually, it shows similarity of distributions of $X$ and $Y$. So, we may redefine the divergence as $1-D_{\alpha,\beta}(f\|g)$. The main problem of the KL divergence is that it does not monotonically map the similarity of $f$ and $g$ to some real value. That is, $f_1$ might be more similar to $g$ than $f_2$ (with point-wise comparison), but has higher KL divergence than $f_2$. However, (1) offers a monotonic mapping, at least in my simulations. Possible application would be in the detection theory, among others. | |
| Dec 2, 2015 at 16:39 | comment | added | Iosif Pinelis | I have added an addendum regarding the edited version of the question. | |
| Dec 2, 2015 at 16:38 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
added 1858 characters in body
|
| Dec 2, 2015 at 3:50 | comment | added | Jeff | Thanks @IosifPinelis for your notes. I have revised the question, and you may revise your answer accordingly. | |
| Dec 1, 2015 at 16:50 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |