Timeline for Entropy and total variation distance
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Sep 28, 2019 at 20:49 | review | Suggested edits | |||
| Sep 29, 2019 at 1:07 | |||||
| Sep 20, 2018 at 4:58 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2018 at 1:40 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2018 at 0:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2018 at 0:47 | comment | added | Iosif Pinelis | It is now shown that the same approach produces the exact bound for any convex function $f$ in place of the function $p\mapsto p\ln p$. | |
| Sep 20, 2018 at 0:42 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2018 at 0:05 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 18, 2018 at 18:04 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 18, 2018 at 17:55 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 18, 2018 at 17:52 | comment | added | Iosif Pinelis | @Algernon : Thank you for your comments. I have now specified that the majorization is understood here in the Schur sense and given a corresponding reference. Also, I have now simplified the proof and no longer use $p_i^*$ for $i>k$. | |
| Sep 18, 2018 at 17:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 18, 2018 at 16:52 | comment | added | Algernon | Also, it should be $p^∗_i\leq q_i$ for $i>k$. | |
| Sep 18, 2018 at 16:52 | comment | added | Algernon | Nice approach! I only didn't understand when you say $(p^*_{k+1},\ldots,p^*_N)$ majorizes the vector $(p_{k+1},\ldots,p_N)$. Both $p$ and $p^*$ are probability vectors and you have already shown that $(p^*_1,\ldots,p^*_k)$ majorizes $(p_1,\ldots,p_k)$. However, I agree that the entropy of $p^*$ must be no larger than the entropy of $p$, which seems to be what you are using. | |
| Sep 18, 2018 at 6:00 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |