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Mar
26 |
answered | A question about the size of a L1 ball |
Mar
24 |
comment |
A question about the size of a L1 ball
Thank you so much for your reply. For question (1), could you please explain in more detail why $\sum\limits_{b=0}^{\sqrt{n}}b^{|\mathcal{X}|-1}$ is approximately equal to $\sqrt{n}\cdot\sqrt{n}^{|\mathcal{X}|-1}$? |
Mar
24 |
comment |
A question about the size of a L1 ball
The third question is here: (3)For the new answer, since the number of balls in any entry of the matrix, including those in the last column, should not be negative, we can not pick any number freely from $[-\sqrt{n},\sqrt{n}]$. So the number of actual pmfs in $\mathcal{T}_{s^*}$ is less than $\sqrt{n}^{(|\mathcal{Y}|-1)\cdot|\mathcal{X}|}$. Therefore, under this constraint, how to understand the new answer? |
Mar
24 |
comment |
A question about the size of a L1 ball
Thank you very much for your answer. But I have three questions as follows: (1) in your old answer, when putting at most $\kappa\sqrt{n}$ balls to $|\mathcal{X}|$ bins and summing for the number of balls from 0 to $\sqrt{n}$ if omitting $\kappa$, I think the total possibilities should be $\sum\limits_{b=0}^{\sqrt{n}}b^{|\mathcal{X}|-1}$. Why you say it is $\sqrt{n}\cdot\sqrt{n}^{|\mathcal{X}|-1}$? (2)Why does "in most cases this distribution will be quite even" so that the number of balls for each row can be obtained by dividing the total balls $\kappa\sqrt{n}$ by $|\mathcal{X}|$? |
Mar
3 |
comment |
A question about the size of a L1 ball
$\mathcal{X}$ is the alphabet of symbols for $X$. $\mathcal{X}^n$ is all the sequence of length $n$ drawn from $\mathcal{X}$. |
Mar
3 |
asked | A question about the size of a L1 ball |
Jan
27 |
accepted | equivalence of 1-norm and relative entropy? |
Jan
27 |
comment |
equivalence of 1-norm and relative entropy?
Yes, you are right. I should have considered the circumstances that $q_i=0$ for some symbol. But what if I put a restriction on $q$ that all $q_i$'s are positive? |
Jan
27 |
answered | equivalence of 1-norm and relative entropy? |
Jan
27 |
revised |
equivalence of 1-norm and relative entropy?
added 7 characters in body |
Jan
27 |
asked | equivalence of 1-norm and relative entropy? |