Timeline for Maximum mutual information of a matrix representation
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Apr 15, 2021 at 13:52 | history | bounty ended | CommunityBot | ||
| S Apr 15, 2021 at 13:52 | history | notice removed | CommunityBot | ||
| Apr 13, 2021 at 10:32 | history | edited | Math_Y | CC BY-SA 4.0 |
added 77 characters in body
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| Apr 13, 2021 at 10:29 | comment | added | Math_Y | You are right. We have a condition that $\mathbf{X}_2$ is bounded. I append it to question. | |
| Apr 13, 2021 at 4:14 | comment | added | Artemy | I believe that in your setup, the MI is unbounded. To see why, let $\mathbf{X}_1 = \mathbf{I}$ with probability 1, so $\mathbf{Y}=\mathbf{X_2} + \mathbf{Z}$. We then have $I(\mathbf{X_1},\mathbf{X_2};\mathbf{Y})=I(\mathbf{X_2};\mathbf{Y})=h(\mathbf{Y}) - h(\mathbf{Y}\vert \mathbf{X_2}) \ge h(\mathbf{X}_2) - h(\mathbf{Z})$. Now the differential entropy $ h(\mathbf{Z})$ is a finite quantity, while the differential entropy $h(\mathbf{X}_2)$ can be arbitrarily large. Hence, the MI can be arbitrarily large. | |
| S Apr 7, 2021 at 12:27 | history | bounty started | Math_Y | ||
| S Apr 7, 2021 at 12:27 | history | notice added | Math_Y | Draw attention | |
| Apr 5, 2021 at 14:39 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Apr 5, 2021 at 11:21 | history | asked | Math_Y | CC BY-SA 4.0 |