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Excellent.

Thanks for such a informative video. I am doing multiphase flow modelling in porous media basically solving Continuity and Darcy equations for oil and water phases. So, during the calculation I ended up vector valued function ( System of Lin. Eqs. with 450 Eqs and 450 Unknowns). Ton calculate Jacobian for this function what would you recommend ? Should I use jacobian function from ForwardDiff ? Thank You.

What program is he using

It's my third day of trying to understand basics of EM and ELBO and I found this video. Now, there won't be a forth. Thankyou

Thank you so much for this tutorial Felix!

I have a question here. Mean Field Approach tells us how to choose the kind of surrogate posterior and eventually we will get the optimal solution for q. However, in the previous lessons, we were assuming that surrogate posterior q is distributed according to a certain distribution and then solving the problem by using maximizing the ELBO. But at that time, we didn't know which type of distribution is the most appropriate one to choose for q. This gave me the illusion that as long as the following assumption is true: surrogate posterior can be divided into smaller independent distribution, the way of maximizing the ELBO to solve the VI problem is meaningless because we can just use Mean Field Approach to solve the VI problem without choosing an arbitrary distribution of q. I am not sure if my understanding is correct.

Great video! Particularly liked the Null hypothesis demonstration in scipy :). Would love more of these coding tutorials from you, as you have a very good way of explaining things inutuively..

I just discovered your channel and... I do not have words, unlimited thanks from France!

Your videos are all so well explained, I would to do the same amazing work one day, thank you!

i love u bro

You saved me! I was so frustrated that I could not understand it, but you video is so clear and understandable!

This video saved my day. Thank you so much!

Very helpful video, thank you so much 😊

HOW OT MAEK THING IN PYTHON: import thing; thing.do();

Thaks for sharing this useful tutorial.

Very interesting. If we wanted to implement for poisson on a membrane could we pretty much keep the original unet image implementation?

understood ✅

4:10 why do you use dy in dL/dy instead of d(y+ef) like you do next in d(y+ef)/de in the chain rule? Isn't this supposed to be the same function that the deriavtive is taken with respect to, as the function that is differentiated with respect to to a variable?

Python is ass💀

bro really went" import fluidSim fluid = fluidSim.water("darkmode") fluid.start()"

Hello, teacher. Your vedios benifit me a lot ！And I have a question，It has been bothering me for a long time. How can something be called adjoint?

awesome!

"fastest" "python"

This is great! Working on a package that uses the adjoint method for implicit differentiation and this video explained things really well :D

oh god, thank you that was the real beset

Many thanks for the great video, I was looking for something along these lines. I have two questions. The first is regarding how you just chose that the term multiplying the Jacobian vanishes. Where do you get the freedom to impose that without this hurting the optimization procedure? From my recollection on Lagrange multipliers, we usually solve for them once we consider the variation of the Lagrangian to be zero, but we don't get much freedom - in fact, whatever they end up being may even have physical meaning, e.g. being normal forces on mechanical systems which are constrained to be on a surface. The second question regards why using Lagrange multipliers should work in the first place. I understand that, if we wanted to find saddle points for the loss then indeed this is the path; but how do we justify using a Lagrange multiplier we found during the minimization process to compute the Jacobian of solution w.r.t to parameters in general?

I was looking at the reference code that you mentioned in the jupyter notebook and found that they coded something weird that I can't understand for 2D. out_ft[:, :, : self.mode1, : self.mode2] = self.compl_mul2d(x_ft[:, :, : self.mode1, : self.mode2], self.weights1) out_ft[:, :, -self.mode1 :, : self.mode2] = self.compl_mul2d(x_ft[:, :, -self.mode1 :, : self.mode2], self.weights2) I don't understand why there are two weights (weights1, weights2) and why they take upper mode1 frequencies. Can you explain this? Thanks for your video.

🤓

Thank you so much for this explanation! I had no problem with taking the derivatives of the functional, and getting ln(p) as a function of lambdas. The real novel ideas (at least for me) are writing ln(p) in terms of complete squares, carefully choosing which order you want to substitute it in the three constraints (first in the mean constraint, then the normalisation constraint, then the variance constraint), and also making simple substitutions like y = x - mu. They seem trivial but I was banging my head before watching this video about how to do these substitutions. Your video was really useful in introducing these small and useful tricks in deriving the gaussian from the maximum entropy principle

I guess a typo at 19.52 that original VI target is argmin( KL(q(z) || p(z|D ))) but it was written p(z,D). Actually p(z,D) is the one we end-up using in ELBO. This can be used to summarize the approach here "ELBO: Well we dont have p(z|D) so instead lets use something we have which is p(z,D) but... Lets show that this is reasonable thing to do"

I think requires_grad is true by default in torch. Never knew jax syntax was so simple. Good one!

Really useful. Thank you!

TGV is a 3D problem though... our c++ code runs this problem for a 64x64x64 grid in 2 seconds

So basically write a c extension got it

You really didn't make anything, though. You just used a library...

Can you say why du/d\theta is difficult to compute? I'm happy to look at references or other videos if that's easier! Thanks for the terrific content.

JAX for math & stats folks. Works just like how you write math in paper Pytorch for IT folks. the backward function in each variables is very helpful in reducing the number of variables & functions to keep in mind

Aaaaand how do we know the joint distribution p(X,Z) ? As said X can be an image from our data set and Z can be some feature like "roundness of chin" or "intensity of smiling". It is bit strange to be able to know jointly p(Image, feature) but not being able to know p(Image) because of multi-dimensional integrals

you lost me at “fastest…in python”

Thanks! I'm learning Bayesian Statistics at uni and didn't fully understand why we need precision.

thanks for your lecture, the pronunciation of inviscid is not [INVISKID] it is simply [INVISID].

*How do do anything in Python:* _Import library that does exactly that_

Could you explain how you came up with the equation following the sentence "Then advance the state in time by..."? Is there any prerequisite to understand the derivation?

Great video! =) Can somebody please explain why we have the joint distribution and why don't have the posterior? I understand that we have some dataset D (images) and maybe we even have their ground truth data Z (like categories, cat, dog, etc..). Does this automatically mean that we have the joint distribution?

Python tutorials: import tutorial tutorial.run()

Super cool as always. Some feedback to enhance clarity - when writing modules (SpectralConv1d, FNOBlock1d, FNO1d), overlaying the flowchart on the right hand side to show the block to which the code corresponds would be really helpful. I felt a bit lost in these parts.

Thank you so much for this series! It has helped me tremendously to understand how automatic differentiation works under the hood. I was wondering if you plan to continue the series, as there are still operations you haven't covered. In particular, I am interested in how the pullback rules can be derived for the "not so mathematical" operations such as permutations, padding, and shrinking of tensors.

Ich finds geil wie du from scratch das einf mal so dahincodest und dabei super erklärst 😅

Just one observation: the functional unconstrained optimization solution gives you an unnormalized function, you said it is necessary to normalize it afterwards. So what does guarantee that this density, but normalized, will be the optimal solution?? If you normalize it, it will not be a solution to the functional derivative equation anymore. Also, the Euler-Lagrange equation gives you a critical point, how does one know if it is a local minima/maxima or a saddle point?

Excellent work! Thanks a lot for sharing.