Timeline for Algorithm for economically sampling method for Gaussian matrix product
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2020 at 13:08 | history | edited | wlad | CC BY-SA 4.0 |
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| Nov 11, 2020 at 13:01 | history | edited | wlad | CC BY-SA 4.0 |
added 267 characters in body
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| Nov 11, 2020 at 12:54 | comment | added | wlad | I think this is a simpler and more general way of looking at it: en.wikipedia.org/wiki/… | |
| Nov 11, 2020 at 12:35 | comment | added | ABIM | Ah, this is very helpful. Thanks ogogmad! | |
| Nov 11, 2020 at 12:32 | comment | added | wlad | It follows from the rotational symmetry of $N(0, \sigma \oplus \sigma \oplus \dotsb \oplus \sigma)$. Consider the case when $x$ is parallel to one of the coordinate axes; it's clear that $a^T x$ follows the same distribution as $N(0, \sigma |x|)$. Now using rotational symmetry of the distribution of $a$, simply change coordinates so that $x$ is parallel to one of the coordinate axes | |
| Nov 11, 2020 at 12:23 | comment | added | ABIM | Actually, this works great. Thank you ogogmad! | |
| Nov 11, 2020 at 12:23 | vote | accept | ABIM | ||
| Nov 11, 2020 at 12:15 | comment | added | wlad | Ah, $a$ follows an axis-symmetric distribution. So I think that to sample from $a^T x$, you need only to sample from $N(0, \sigma)$ and multiply by $|x|$. Does that make sense? | |
| Nov 11, 2020 at 12:10 | comment | added | wlad | @Zorn'sLama Is there a way to sample from $a^T x$ where $a$ is a vector of iid samples from $N(0, \sigma)$? I'll try and think about this | |
| Nov 11, 2020 at 12:07 | comment | added | ABIM | I like this idea. However, it may take a long time to loop over. Would you happen to know of another way? | |
| Nov 11, 2020 at 12:03 | history | answered | wlad | CC BY-SA 4.0 |