Aryeh Kontorovich
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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 $$. Apr 26 comment How to calculate \langle v,w\rangle based only on \langle v,x_i\rangle and \langle w,x_i\rangle? How do you use Gramâ€“Schmidt if you don't have access to the explicit representation (i.e., the numerical entries) of the x_i? You are only given 2n numbers: a_i= and b_i=. The goal is to compute$$ 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?