Timeline for Finding discrete entropy via differential entropy
Current License: CC BY-SA 3.0
7 events
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| Jan 20, 2016 at 1:37 | comment | added | user75274 | I think the proof of the formula relating differential and discrete entropy in the multi-dimensional case is exactly the same -- in fact the only change needed in the argument is the replacement integration with respect to $dx$ by integration with respect to $dx_1 ... dx_n$ (the extra factor of $n$ in front of $\log t$ comes from the joint variance of $G_1,\dots,G_n$). To see the behavior when you apply your matrix $M$, just use the formula to compute $h((\sum_{i} M_{ij} Y_i)_j )$. | |
| Jan 18, 2016 at 11:48 | comment | added | Simd | Thank you this 1d analysis. The 1d case is clear and I was in fact happy with it before. I would be very grateful if you could show how you can apply the same reasoning to the multidimensional $Mv$. Part of my confusion is what the approach would give if $M$ had fewer rows than columns. This presumably would then depend crucially on the entries in $M$. But even understanding the $n$ by $n$ case would be a great start. | |
| Jan 17, 2016 at 20:50 | history | edited | user75274 | CC BY-SA 3.0 |
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| Jan 16, 2016 at 6:39 | history | edited | user75274 | CC BY-SA 3.0 |
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| Jan 15, 2016 at 14:36 | comment | added | Simd | Thank you but I am not clear on some details. As a first trivial question, doesn't $\log{t}\to -\infty$ as $t$ tends to $0$? How do you get the entropy of $n$ from the RHS? | |
| Jan 7, 2016 at 20:50 | comment | added | Simd | Would you mind spelling out a little more what you get in the end? In particular, do you get the correct discrete entropy of $n$ this way? | |
| Jan 5, 2016 at 18:17 | history | answered | user75274 | CC BY-SA 3.0 |