Thank you! Glad this is working for you

THank you and I will! I got something big in the works :)

@@Mutual_Information Do you plan on doing one for EM derivation of GMMs?

@@karanshah1698 EM yes, GMMs, yes eventually. Using them together?? No I didn’t think of that, hm

Human transforms short-term memory to long-term memory by understanding and prediction.

This means a lot getting your comment here. Much appreciated! And yes! There are unfortunately rigor qualifications that I omit to keep the vid light. In the case of integrability, I hadn’t thought of that, so thanks for pointing it out :)

Glad it was helpful!

I appreciate that!

Thanks Sumaya! More coming :)

Thanks - great to have you! This was my first vid. I've gotten a lot of useful feedback since, but glad this one still lands

Thank you! Happy to help

Yes! The EM algorithm will be covered, but later this year. If you're curious immediately, I linked to some sources in the description where Jensen's Inequality is used. In Cover's book, there is a section "Jensen's Inequality and Its Consequences" which show how foundational it is for Information Theory.

Hey thanks and to answer your question, I stick together a bunch of graphs made in Altair using a personal library. Altair is very nice plotting library

Looks like he is using manim made by 3blue1brown

There's no need to put yourself down in such a way. You can be thankful for the content this guy is putting out on YT by liking, subscribing and hitting the share buttom...stop dragging yourself over the coals.

First comment :) will do!

lol old video will lots of energy.. I've chilled out a bit since, but thank you

Course man - glad you liked it

Excellent, thank you!

Yea I’ll do a video on the EM algorithm, where this shows up. Also, variational inference, eventually. And I’m happy to hear that! I hope you’re right but we’ll see.

Glad you’re here! His channel is a huge inspiration. And yep, concave functions you get the opposite. The neg of a convex I’d a concave function and that deserves the inequality.

Yea it shows up a lot. Glad you enjoyed it

Thank you! More coming - one every 3 weeks.

Glad you enjoyed it!

I got something good cookin :)

Glad you like it!

And thank you too Satish!

Thank you very much!

Thanks! And I do have plans to make a video on variational inference but it may take awhile. There are a few videos in front of it. But it’s coming!

For sure - If you'd like, you can do me a solid and anyone into ML/stats about the channel :)

Hm, sorry but that's unlikely. It's just too specific. The topics I've picked are already fairly niche. If I go into a very specific subtopic, it'll appeal to very few folks (unless there is something particularly fascinating about it)

Thank you - it means a lot !

Thanks for the love! Answered you on Twitter :)

Yes it does!

Yep, then that would be a concave function and the inequality would be reversed. A pretty common example of that is the log(x) function.

My question was not answered by the author, maybe you can help me. My doubt is precisely about the equality holding for any straight line... why it is true? I can understand it holds for linear functions of type f(x) = c.x, in the sense of addition and multiplication conservation -> hence f(E(x)) = E(f(x)). Functions of the type f(x) = ax+b are straight lines, but not linear funcions in these sense, so we cannot prove that f(E(x))=E(f(x)). Try to use f(x) ~ exp(k) and the transformation Y = ax + b, you'll see that f(E(x))=a/k+b and E(f(x))=exp(kb/a)*a/k, which do not hold for any straight line, but just for b=0.

I’m not sure what you’re saying. The equality is satisfied when f is an affine transformation. This is trivial because E is a linear operator: E(f(X)) = E(aX+b) = a E(X)+b=f(E(X)) where the first step applies the definition that f is affine (a straight line), the second, that E is linear, and the third using again the definition of f being affine. In your example you’re mixing up letting f be an exponential or letting it be an affine transformation, so you get something weird. You can’t apply both transformations at the same time, that is not something that Jensen inequality talks about in any way. If the function is convex, you get an inequality. If the function is strictly convex (unless X is constant a.s.) you get strict inequality. And in the opposite edge case that the function is affine (which is also convex), you get strict equality.

@@rocamonde Of course you are correct, in my example I made a mistake calculating E[f(X)], for that reason the equality does not hold. My approach was to see the theorem from the affine functions properties, but in fact is much more simple to see it from the expectation linearity. Thank you, your explanation was clear!

Glad you enjoyed it!

Thanks!

Thank you! I’ve heard that book recommended a few times but have never checked it out. I’ll order it!

Thank you! 3rd donation ever :)