Timeline for Probabilistic Johnson-Lindenstrauss Lemma for arbitrary points
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2013 at 21:04 | comment | added | Xorwell | I definitely allow to take into account that $f$ is chosen randomly, at first. I would like to keep $f$ fixed for each test $z:=z_1,\ldots, z_i,\ldots \in \mathbb{R}^d$ | |
| Dec 28, 2013 at 20:55 | history | edited | Xorwell | CC BY-SA 3.0 |
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| Dec 28, 2013 at 18:46 | comment | added | Bill Johnson | Do you want an estimate dependent only on $d$, $k$, and $|X|$? Or do you allow to take into account that $f$ is chosen randomly? In the first case, you can't say much of anything; in the second case, Dustin's comment is a good answer. | |
| Dec 28, 2013 at 17:23 | history | edited | Xorwell | CC BY-SA 3.0 |
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| Dec 28, 2013 at 17:03 | answer | added | Dustin G. Mixon | timeline score: 1 | |
| Dec 28, 2013 at 16:32 | comment | added | Xorwell | I want to fix $f$, eventually compute $f$ w.r.t. to $X$ but then fix $f$. At this point use the randomness in $z$. Also consider that, for the fixed $f$, I would like to test many (at least $\omega(\text{poly}(|X|)$) random $z$. | |
| Dec 28, 2013 at 16:17 | comment | added | Dustin G. Mixon | Let $f$ be a random projection. Then it will be JL with high probability, regardless of $X$. If I make $X$ a little larger (by including $z$), $f$ will still be JL with high probability. Is this useful to you, or do you want to fix $f$ and only use the randomness in $z$? | |
| Dec 28, 2013 at 16:05 | comment | added | Xorwell | I tried rephrasing. Hope this clarify. If not, what is more obscure? | |
| Dec 28, 2013 at 16:04 | history | edited | Xorwell | CC BY-SA 3.0 |
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| Dec 28, 2013 at 15:44 | comment | added | Dustin G. Mixon | Don't get me wrong - I read what you already wrote, but it is not clear what you are asking. Consider rephrasing the question. | |
| Dec 28, 2013 at 15:36 | comment | added | Xorwell | Hi D., my question would be: how would one treat arbitrary vectors ? Is the guess true ? | |
| Dec 28, 2013 at 15:36 | history | edited | Xorwell | CC BY-SA 3.0 |
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| Dec 28, 2013 at 14:44 | comment | added | Dustin G. Mixon | What is your question exactly? | |
| Dec 28, 2013 at 13:24 | history | edited | Xorwell | CC BY-SA 3.0 |
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| Dec 28, 2013 at 13:16 | history | asked | Xorwell | CC BY-SA 3.0 |