Timeline for Dimension-free sample complexity for estimating Gaussian covariance
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Aug 4, 2022 at 3:54 | comment | added | Yaroslav Bulatov | good catch....that seems to be the case Theorem 9.2.4 | |
| Aug 4, 2022 at 3:28 | comment | added | Jason Gaitonde | Unless I'm missing something, doesn't Vershynin's Theorem 9.2.4 address this? | |
| Aug 4, 2022 at 3:15 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| S Jun 23, 2021 at 22:03 | history | bounty ended | CommunityBot | ||
| S Jun 23, 2021 at 22:03 | history | notice removed | CommunityBot | ||
| S Jun 15, 2021 at 21:03 | history | bounty started | Yaroslav Bulatov | ||
| S Jun 15, 2021 at 21:03 | history | notice added | Yaroslav Bulatov | Draw attention | |
| Jun 15, 2021 at 21:01 | comment | added | Yaroslav Bulatov | The most interesting result would be a tight bound for unrestricted $\Sigma$, but special cases might be interesting too | |
| Jun 15, 2021 at 21:00 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| Jun 15, 2021 at 20:59 | comment | added | Yaroslav Bulatov | I agree terminology could be ambiguous. I first saw "dimension-free" used in this way in Nick Harvey's notes cs.ubc.ca/~nickhar/W12/Lecture15Notes.pdf . Without context perhaps a better way would have been to say "depending on effective dimension, independent of ambient dimension". | |
| Jun 15, 2021 at 14:04 | comment | added | Gilles Mordant | Sure. For your question to be clearer, it might be better to state that dimension-free in your question refers to the ambient space and not the intrinsic dimension. Note also that the case you are referring to is extremely restrictive. What set of matrices $\Sigma$ do you want to consider ? | |
| Jun 14, 2021 at 16:55 | comment | added | Yaroslav Bulatov | For a Gaussian with covariance a multiple of identity, you can drop the $\log n$ part, so the sample complexity becomes dependent only on the intrinsic dimension $r$ and not on the ambient dimension $n$ | |
| Jun 14, 2021 at 12:06 | comment | added | Gilles Mordant | If you want a bound that is as tight as possible, you certainly need to use the peculiarities of the Gaussian case. Did you have a look into the Wishart distribution and how it concentrates around its mean ? I do not believe that you can get rid of the dimension. | |
| Jun 11, 2021 at 17:03 | history | edited | Yaroslav Bulatov | CC BY-SA 4.0 |
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| Jun 11, 2021 at 16:33 | history | asked | Yaroslav Bulatov | CC BY-SA 4.0 |
