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Apr
26 |
comment |
How to calculate $\langle v,w\rangle$ based only on $\langle v,x_i\rangle$ and $\langle w,x_i\rangle$?
I think you'll also need information on $<x_i,x_j>$. |
Apr
26 |
comment |
How to calculate $\langle v,w\rangle$ based only on $\langle v,x_i\rangle$ and $\langle w,x_i\rangle$?
How do you use Gramâ€“Schmidt if you don't have access to the explicit representation (i.e., the numerical entries) of the $x_i$? You are only given $2n$ numbers: $a_i=<v,x_i>$ and $b_i=<w,x_i>$. The goal is to compute $<v,w>$ as a function of these $2n$ numbers alone. As Boaz mentioned, you must assume that the $x_i$ are a basis. In this case, I think you can recover the $v,w$ exactly -- at least the number of variables matches the number of unknowns. |
Apr
20 |
answered | What is the order of the constant $K$ in the multidimensional Dvoretzky-Kiefer-Wolfowitz inequality($Ke^{-c z}$)? |
Apr
7 |
revised |
What do you call the collection of all sets shattered by $F$?
added 66 characters in body |
Apr
7 |
asked | What do you call the collection of all sets shattered by $F$? |
Apr
6 |
comment |
Sharpened Pinsker inequality for special case
Just a quick comment: the conjecture (now theorem in light of Iosif's answer) is indeed true for all $x\in[0,1]$. However, my weaker bound with $2.1\sqrt n x$ doesn't hold on all of $[0,1]$. |
Apr
6 |
comment |
Sharpened Pinsker inequality for special case
Beautiful, @Iosif Pinelis! |
Apr
6 |
accepted | Sharpened Pinsker inequality for special case |
Apr
5 |
asked | Sharpened Pinsker inequality for special case |
Mar
28 |
comment |
Metric analogues of bounded variation
Thanks again. I guess there's a reason why the Hardy-Krause extension to higher dimensions is so complicated. |
Mar
26 |
comment |
Metric analogues of bounded variation
@WillieWong One last attempt before giving this a rest. What if we consider an $\epsilon$-net (i.e., minimal cover/maximal packing), and then take $\mathcal{P}_n$ to be the Voronoi regions induced by the net points? |
Mar
22 |
comment |
Metric analogues of bounded variation
Very nice example, @WillieWong, and thanks Suvrit for the link. I was also pointed to arxiv.org/pdf/1301.6897v1.pdf . So I guess it's time to quite amateur conjecturing and start reading... |
Mar
22 |
revised |
Metric analogues of bounded variation
added 625 characters in body |
Mar
22 |
comment |
Metric analogues of bounded variation
Thank you for that example, @MartinHairer. Rather than risk further embarrassment with additional edits, let me try to continue in the comments. Suppose I define $\mathcal{P}_n$ to be the Voronoi partition induced by some $n$ points, and define the variation to be the supremum over all $\mathcal{P}_n$. Does this still admit pathological examples? |
Mar
22 |
comment |
Metric analogues of bounded variation
You're of course right, @AugustCleaner! I tried to fix this in the edited version. |
Mar
22 |
revised |
Metric analogues of bounded variation
added 431 characters in body |
Mar
22 |
asked | Metric analogues of bounded variation |
Feb
8 |
comment |
measure of the distance between two joint distributions
See this paper by Gibbs and Su "ON CHOOSING AND BOUNDING PROBABILITYMETRICS" math.hmc.edu/~su/papers.dir/metrics.pdf |
Feb
7 |
awarded | Custodian |
Feb
7 |
reviewed | Approve Weyl-type inequality for non-Hermitian matrices? |