Lagrange Multipliers : Data Science Basics

How do we use Lagrange Multipliers in Data Science?

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[robertleo]

Hey man these videos are great, you deserve more attention

[jeonghwankim]

Great explanation man. Your explanation is way more intuitive than most of the videos out there.

[diegososa]

This was fantastic. You have a gift for teaching.

[jameswang]

Quick question: at 1:29 the matrix S you give is not symmetric, but when you do the Lagrange multipliers at 7:14 you use the result that the matrix derivative of u^TSu is 2Su which (in your other video "Derivative of a Matrix") you derived for the 2x2 case assuming the matrix was symmetric. Does this result hold for the non-symmetric case? If so, how would I go about showing that? If not, what can be done for the non-symmetric case?

[BhuvaneshSrivastava]

This is great explaination. Thanks a ton.
It would be great if you could make a video on maths behind Logistic Regression as well.

[DistortedV]

Just subscribed I like how you explain things and videos are very “snackable.”

[fabriai]

Thanks a lot for the video. I hadn't realized the relationship between lagrangians and eigenvectors.

[mrFilip]

Awesome video mate! It makes so much sense

[momaalim]

Thank you very much sir. Really appreciate you making these super helpful videos.

[ankitsrivastava]

Great videos.. very well explained.. thank you

[supriyamanna]

your intuition level is just A+. I think you should do ds and ml full time

[alejrandom]

6:45 BIG mistake right here. This derivative ONLY holds when S is symetric, which is NOT true for this case. The general solution is (S+S^T)u, which is easy to show that works. Other than that, good video ;)

[turkish]

very clear explanation. good job my friend

[thirumurthym]

thanks for this nice crisp video. If it is minimisation problem - means looking for minimum eigen value and its vectors? Im looking forwad to see the video to detail the basis of lagrange multipliers. Thanks once again.

[alexrvolt]

I'd like to have a deeper view about this interpretation.
The interpretation I understand intuitively is that of wikipedia, where the gradients of the goal function and of the constraint function have to be colinear.
I like the eigenvalue-based interpretation, but something is unclear for me: in the present case, you chose the constraint function in such a manner that we get the simplification that enables to write things as an eigenvalue problem.
It's harder for me to interpret it in a more general manner, with any form of goal/constraint functions....
Moreover, what about the fact that we also need to cancel d(Lagrangian function)/d(lambda)? I'm confused about how this could be related to eigenvalue....

[EW-mbih]

How do you choose the "order" of the constraint in your new function?
I mean how do you choose to write:
uTSu + \lambda(1-uTu) and not
uTSu + \lambda(uTu-1) ?

[paulntalo]

Now that you have shown us the theoretical parts I request that it would be better to now start building the practical code in Python for each individual video. That would help cause theory to meet with code.

[amnont]

6:00 didn't understand why lambda*(1-uTu) isn't 0, since we defined uTu = 1, didn't we?

[HansKrMusic]

thank you. To me, there is still something fishy going on - you say that you'd want to take the biggest eigenvalue of matrix S and find its corresponding eigenvector - in order to "maximize the success". Those eigenvalues and -vectors are complex-valued (a pair of a complex number and its conjugate), and we can't just compare complex numbers. So the best direction would be spiraling outwards?

[vinceb]

u.T S u is a formula I've encountered several times, can anyone help me what it is actually? It seems we're projecting the linear transformation of u onto itself, but what does that tell us?