Linear Regression

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4 жыл бұрын

Linear regression is a cornerstone of data-driven modeling; here we show how the SVD can be used for linear regression.
Book PDF: databookuw.com/databook.pdf
Book Website: databookuw.com
These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com/Data-Driven-Sc...
Brunton Website: eigensteve.com
This video was produced at the University of Washington

Пікірлер: 33

@Ash-bc8vw 2 жыл бұрын

I don't think anybody is teaching LR with respect to SVD on KZfaq right now, hence this video is more informative! Loved it immediately subscribed

@nikosips 4 жыл бұрын

Those videos are the best resource for someone who wants to understand data driven models! Thank you very much for your work from an engineering student!!

@appliedmathness8397 3 жыл бұрын

I love thiese videos! But in this one you point out the "squared projection error" while showing the segment going from the biased line to the outlier (like in PCA); instead in case of linear regression residuals should be vertical lines.

@SoroushRabiei 4 жыл бұрын

Dear professor, you're a great teacher! Thank you so much for these videos.

@patrickxu8795 2 жыл бұрын

The lecture is so clear and well-organized! IT IS IMPRESSIVE!!!!

@Chloe-ty9mn Ай бұрын

i've been watching all the videos in this chapter and this is the one that got me to cave and purchase the book!! i was so surprised to see that it was so affordable. thank you and your team so so so much for the high quality accessible information

@dmitrystikheev3384 3 жыл бұрын

I was looking for copper, but found gold! Boss, excellent as always. Love your way of conveying the material. I hope you will continue presenting more topics on statistics, cause in the multivariate case it can become really intimidating. Best regards from Russia!

@shakibyazdani9276 3 жыл бұрын

Absolutely awesome series, I will finish the whole series today:)

@Eigensteve 3 жыл бұрын

Hope you enjoy it!

@vahegizhlaryan5052 Жыл бұрын

I am honestly surprised(just accidentally discovered this channel) why this coolest recourse is not popular among KZfaq algorithms

@hengzhang7039 4 жыл бұрын

Thank you sir, your courses are awesome!

@ParthaPratimBose 3 жыл бұрын

Hi Steve, I am a pharmaceutical data analyst, but you're just outstanding

@Eigensteve 3 жыл бұрын

Wow, thanks!

@saitaro 4 жыл бұрын

This is gold, professor!

@motbus3 3 жыл бұрын

besides the very awesome explanation, the book is awesome and he writes mirrored as it was nothing 😄

@linnbjorkholm9237 Жыл бұрын

Wow! Great video! I really liked your shirt, where is it from?

@Eigensteve Жыл бұрын

It’s a Patagonia capilene. My favorite shirt. I almost only wear them

@a.danielhernandez2839 3 жыл бұрын

Excellent explanation!, What happens with the y-interception of the line? Is it b?

@sachavanweeren9578 3 жыл бұрын

very nice series ... though it has been a while and I might be a bit rusty on my math. But if I recall correctly there is nowhere an explicit link made between the SVD and least squares. It is explained that the there is an SVD and with a theorem that this was the best one in some norm. But I have not seen an explicit link with ols. Would be nice if that would be more explicit in the video series...

@user-ih4mv5hl9i 8 ай бұрын

Interesting. In the first lecture of this series, individual faces (i.e. people) were in the columns, but a face was really a column of many pixels. In this lecture, people are in the rows. So each use of SVD is different. And each setup of a data matrix is different.

@engr.israrkhan 4 жыл бұрын

sir great teacher you are

@udriss1 2 жыл бұрын

Hello. In your book DATA DRIVEN SCIENCE & ENGINEERING page 24, relation (1.26), you express the matrix B. In this relation you must write: B = X - X bar and not as one can read B = X - B bar. With here X bar which is the matrix of means.

@kindleflow 4 жыл бұрын

Thanks

@Martin-iw1ll 8 ай бұрын

In mechanics, overdetermined is named statically indeterminate

@clickle23 3 жыл бұрын

Can you explain why in the example at the end, U = a/|a|, is it because U has the only one eigen vector of matrix AA(transpose), which is just itself?

@spidertube1000 3 жыл бұрын

Good vid bruh

@anilsenturk408 4 жыл бұрын

How's it going?

@robsenponte3308 2 жыл бұрын

Cool

@moshuchitu203 2 ай бұрын

by cross referencing kzfaq.info/get/bejne/q8ecoNyLzrbXaas.html, one can clearly see the slope derived in the end is nothing but "covariance (a, b)/variance(a)"

@philrincon Жыл бұрын

Is he writing in the reverse?

@ralfschmidt3831 3 жыл бұрын

I am slightly confused: the orthogonal projection of b onto a should minimize the distance between b and its projection - which is ORTHOGANAL to the span of a. If I remember correctly, the minimum least squares, however, should minimize the VERTICAL distance between the projected and the original point. I am sure there is something wrong with my assumptions but maybe someone can point me in the right direction