Regression and Ax = b: Over- and under-determined systems

[@HassanKhan-cs8ho]

I ABSOLUTELY LOVE THE WORK YOU AND STEVEN BRUNTON HAVE DONE!!!! YOU ARE LEGENDS!!!! LOVE YOU!

[@ad2181]

He's setting a new standard for teaching Linear Algebra. He's GQ dress with the suite too. Enjoy the lectures they are Golden.

[@gaelparfait4269]

Great stuff thanks a million professor Kutz. It is precise and concise, I can't imagine the number of souls you guys are saving out there

[@tinkeringengr]

This channel is great! keep up the great work, fundamentally changing civilization.

[@djtovys]

First comment. I admired the Dr. Kutz. And this video is grateful. Thanks Dr. Kutz

[@anilrao6]

thank you Prof. Nathan Kutz

[@dmitriiandreev8320]

The best quality education

[@CTSSHAH]

thank you for a wonderful book and video series

[@anothermlstudent1458]

Thank you very much Nathan for the great video! When in 3:37 you say "you cannot satisfy Ax = b, is overdetermined", if I imagine the case where some rows may be duplicated in my data or for some reason some rows happen to be a linear combination of the others I may get a "tall" matrix (or and overdetermined system) that may have a solution/s. In short, following the same definition of overdetermined as in en.wikipedia.org/wiki/Overdetermined_system, you can have an overdetermined system with a solution. Do you use a different definition of under- overdetermined? (for instance, only taking into consideration the number of equations after reduction?) or you are just focusing on what you assume to be the most common case in a data matrix (to not present duplicated or dependent rows? Thank you for the clarification =)

[@azoj777]

no, you are correct - in an overdetermined system you'll only have a solution if b is in the span of A, and since the column vectors of A belong to R^n and n is significantly greater than m, the col vectors of A only span some subspace of R^n (a small subspace given that n is significantly greater than m). b is also a vector in R^n but it's likely that b is not in the subspace that A spans, so it's likely we don't have a solution.

[@anilcelik16]

Thank you for the effort

[@ОльгаКудрявцева-ы3р]

how do you do that?

[@VIVEKPANDEYIITB]

How does solver determine which variables are useful in case of l1 norm? Also, how do we prove theoretically that l1 promotes sparsity? Anyone?

[@TheRsmits]

Watching this again and realized the problem of over-fitting is analogous to the 'no true Scotsman' fallacy in philosophy where someone has given themselves so many parameters that they can fit any data.

[@palzhanov]

👍

[@HD-qq3bn]

Respect you

[@ErnestoMendoza-oo1fq]

The MathLab and Python solutions for the undetermined case, panel (D) do not match.

[@mohammadaminmousavi5011]

GREATTT!