Timeline for Bounding sum of multinomial coefficients by highest entropy one
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2010 at 19:37 | comment | added | Yaroslav Bulatov | I added "proof by picture" that the binomial proof can be generalized...what's missing is an explicit characterization of the set of p's where H(p,q)>H(q) | |
| Aug 18, 2010 at 16:52 | comment | added | Leandro | You right. I did not reply before, because I am investigating the generalization of the case two inequality. I have one, but it also seem stupid as my previous argument. If I have time I will think about it little bit more. | |
| Aug 18, 2010 at 16:32 | comment | added | Yaroslav Bulatov | The difference between you proof and the one I linked is that they base their proof on an entropy inequality that holds for a range of coefficients. In your case, your starting inequality holds for just one coefficient, so it can be replaced by equality. It gives a bound on a multinomial coefficient in terms of it's entropy. There's at most (n+1)^k coefficients in any set E (+1 comes if we allow 0's), so we can bound the sum over these coefficients over the set by (n+1)^k Exp[n H^*] .... that's the same as Sanov's theorem | |
| Aug 18, 2010 at 3:24 | comment | added | Yaroslav Bulatov | Also, it seems your set E contains at most 1 element | |
| Aug 18, 2010 at 2:51 | comment | added | Yaroslav Bulatov | Is it essential to disallow 0's in the coefficients? Allowing 0's would allow to relate to existing bounds, like the one I linked | |
| Aug 18, 2010 at 2:23 | history | answered | Leandro | CC BY-SA 2.5 |