Timeline for An inequality of KL Divergence for two different distributions passing through a same channel
Current License: CC BY-SA 4.0
13 events
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| Mar 18, 2021 at 15:21 | comment | added | Christian Chapman | I'm guessing that you're trying to formalize a notion similar to this: $${}$$ "$X_1$ and $X_2$ are like $X$, but with different types of noise. $Z$ is a mixing of $X_1$ and $X_2$. There is also some process $Y(\cdot)$ that acts on RVs that live in $\mathcal{X}$. Can I always mix $Z$ so that I learn less about $Y(Z)$ from $Z$ than I learn about $Y(X)$ from $X$?". $${}$$ The answer seems like yes, but what you've written isn't quite the right formalization yet. In particular you need to more closely specify the nature of $X_1$ and $X_2$ (and more cleanly specify the entire problem). | |
| Mar 18, 2021 at 15:09 | comment | added | Christian Chapman | What's more, as you've written it, the LHS $D(P_{Y|Z}|P_{Y_2})$ is going to be a random variable depending on $Z$ and the RHS is a RV depending on $X$. I'm not sure that this is what you are really after. | |
| Mar 18, 2021 at 14:59 | comment | added | Christian Chapman | Math_Y, your definitions are too lax. Nothing about X1, X2 enforces that Z resemble or preserves information about X in any way. This leaves the two sides of your desired inequality unrelated. | |
| S Sep 12, 2020 at 22:02 | history | bounty ended | CommunityBot | ||
| S Sep 12, 2020 at 22:02 | history | notice removed | CommunityBot | ||
| Sep 11, 2020 at 10:39 | history | edited | Math_Y | CC BY-SA 4.0 |
edited body
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| S Sep 4, 2020 at 20:50 | history | bounty started | Math_Y | ||
| S Sep 4, 2020 at 20:50 | history | notice added | Math_Y | Draw attention | |
| Sep 2, 2020 at 21:17 | history | edited | Math_Y | CC BY-SA 4.0 |
added 221 characters in body; edited tags
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| S Sep 2, 2020 at 16:22 | history | suggested | RobPratt | CC BY-SA 4.0 |
corrected spelling in title
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| Sep 2, 2020 at 15:58 | comment | added | Iosif Pinelis | Can you restate your question in formal mathematical terms, without using such terms as "channels", "cross", and "produce"? Also, even though one could guess what you mean by $\bar\lambda$, can you still define this symbol? Also, by $X\in\mathcal X$ you apparently mean "$X$ takes values in $\mathcal X$", which is of course quite different from $X\in\mathcal X$. | |
| Sep 2, 2020 at 15:56 | review | Suggested edits | |||
| S Sep 2, 2020 at 16:22 | |||||
| Sep 2, 2020 at 15:02 | history | asked | Math_Y | CC BY-SA 4.0 |