Timeline for What is the relationship between the Fisher Information and the Fisher Information metric?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2018 at 23:38 | comment | added | Deane Yang | Your last comment is the correct one. If $X = \mathbb{R}$ and $f(x,\theta) = f(x-\theta)$, then $g_f^{FR}$ is a $1$-by-$1$ matrix equal to $I_f$. | |
| Nov 29, 2018 at 16:00 | comment | added | S.Surace | I will add something later when I have more time. | |
| Oct 29, 2018 at 2:03 | comment | added | Gabe K | I think this is right and that probably not too much else can be said. Thanks for thinking on it. If you want to expand on it, I'll definitely be interested in reading your answer. | |
| Oct 27, 2018 at 13:56 | comment | added | S.Surace | After spending some more times with these concepts, I think the deepest that I can say so far is: the Fisher information functional is the derivative of the entropy along the heat semigroup, while the Fisher-Rao metric is the Hessian of the relative entropy $H(\nu||\mu)$ wrt. the first argument. I don't know whether this helps your quest. If you want, I can add another answer to expand on this. | |
| Jul 11, 2018 at 2:24 | comment | added | Gabe K | Thanks for bringing that up. That's actually exactly what I've been looking into recently. It appears this yields some interesting relationships, but let me work out the details before I say anything too publicly. | |
| Jul 10, 2018 at 20:51 | comment | added | S.Surace | Have you heard about the fact that the Fisher information functional is the derivative of entropy along the heat semigroup? | |
| Jun 7, 2018 at 19:41 | answer | added | S.Surace | timeline score: 1 | |
| Jun 6, 2018 at 13:01 | comment | added | Gabe K | Thanks for the reference. However, that question is entirely about the second type of Fisher information, where the derivatives are in the statistical manifold and doesn't use the first type, where the derivatives are in the state space. | |
| Jun 5, 2018 at 18:39 | comment | added | SMD | Possibly relevant: stats.stackexchange.com/questions/154724/… | |
| Jun 5, 2018 at 16:04 | review | First posts | |||
| Jun 5, 2018 at 16:08 | |||||
| Jun 5, 2018 at 15:51 | history | asked | Gabe K | CC BY-SA 4.0 |