/sci/ - Science & Math » Thread #12815770

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machine learning

Anonymous Wed 10 Mar 17:04:03 2021 No.12815770 View Reply Original Report

Quoted By: >>12815797 >>12815800 >>12815941 >>12816534 >>12816544 >>12817109

What's a more important concept in machine learning -Hilbert Space or Banach Space?

Anonymous

Anonymous Wed 10 Mar 2021 17:16:23 No.12815797 Report

Quoted By:

>>12815770
That's a weird kind of question.
I mean what's more important to houses, windows or glass?

Anonymous

Anonymous Wed 10 Mar 2021 17:19:09 No.12815800 Report

Quoted By:

>>12815770
I don't know about machine learning but every Hilbert space is L^2 while there are plenty of interesting Banach spaces. So Hilbert spaces are far more important.

Anonymous

Anonymous Wed 10 Mar 2021 18:11:26 No.12815941 Report

Quoted By: >>12817105

>>12815770
All Hilbert spaces are Banach spaces so that makes Banach spaces more important by default.

Anonymous

Anonymous Wed 10 Mar 2021 21:01:03 No.12816534 Report

Quoted By:

>>12815770
probably vectorization in kernel hilbert spaces but what do I know..?

Anonymous

Anonymous Wed 10 Mar 2021 21:02:45 No.12816542 Report

Quoted By:

Why do you even want to know the math? All you need is the packages and a training set.

Anonymous

Anonymous Wed 10 Mar 2021 21:03:29 No.12816544 Report

Quoted By:

>>12815770
any hilbert space is a banach space, but saying which is more important isn't really how you should go about thinking about them

Anonymous

Anonymous Wed 10 Mar 2021 23:52:14 No.12817105 Report

Quoted By:

>>12815941
>all generalizations of structures are more interesting
Patently false. Imagine thinking that magmas are more interesting than groups.

Anonymous

Anonymous Wed 10 Mar 2021 23:53:25 No.12817109 Report

Quoted By: >>12817112

>>12815770
Both are interesting, but Hilbert spaces are more immediately motivated in machine learning because of ideas like RKHS

Anonymous

Anonymous Wed 10 Mar 2021 23:55:22 No.12817112 Report

Quoted By:

>>12817109
Actually eh, maybe not the best example since RKBS exists too. I stand by the original sentiment though - the nice structure of Hilbert spaces is compatible with many natural problems in ML that you don’t need that much expertise to analyze. Just start with Hilbert and generalize out.

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