Timeline for Does this KL divergence inequality hold?
Current License: CC BY-SA 4.0
10 events
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| Sep 24, 2023 at 16:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 24, 2023 at 15:34 | comment | added | Jiacai Liu | OK, thanks again. | |
| Sep 24, 2023 at 15:32 | comment | added | Iosif Pinelis | @JiacaiLiu : I suggest you post your latter question in a separate post. | |
| Sep 24, 2023 at 15:22 | comment | added | Jiacai Liu | Thanks for your help. Since the conjectured inequality does not hold in the opposite direction, can we find a function of $\beta$ and replace the $\beta$ in the RHS of the conjectured inequality with it so that the new inequality can hold in the opposite direction ? For example, the new inequality can be $KL(y || q ) \le \sqrt{\beta} * KL(p || q)$ | |
| Sep 24, 2023 at 13:28 | comment | added | Iosif Pinelis | @JiacaiLiu : The answer to this is also no. I have added details on this to the answer. | |
| Sep 24, 2023 at 13:26 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 24, 2023 at 7:01 | comment | added | Jiacai Liu | I wonder whether this inequality always hold for the inverse direction ? That is KL(y || q ) <= \beta * KL(p || q) | |
| Sep 24, 2023 at 5:29 | vote | accept | Jiacai Liu | ||
| Sep 24, 2023 at 5:28 | comment | added | Jiacai Liu | Thanks for your counter-example. It's very helpful to me. | |
| Sep 24, 2023 at 2:05 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |