The Chain Rule

Рет қаралды 237,611

Күн бұрын

The Chain Rule is a method for finding complex derivatives and is used all the time in Statistics and Machine Learning. This video breaks it down into its two simple pieces and shows you how they easily come together. We then use the Chain Rule to solve a common Machine Learning problem - optimizing the Residual Squared Loss Function.
English
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Portuguese
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0:00 Awesome song and introduction
2:02 A super simple example
6:32 A slightly more complicated example
9:16 The Chain Rule when the relationship is not obvious
11:47 The Chain Rule for the Residual Sum of Squares
Corrections:
13:05 When the residual is negative, the pink circle should be on the left side of the y-axis. And when the residual is positive, the pink circle should be on the right side.
#StatQuest #TheChainRule #DubbedWithAloud

Пікірлер: 446

@statquest 2 жыл бұрын

Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/ Corrections: 13:05 When the residual is negative, the pink circle should be on the left side of the y-axis. And when the residual is positive, the pink circle should be on the right side.

@adolfocarrillo248 Жыл бұрын

This is an amazing explanation!!! Thanks

@statquest Жыл бұрын

@@adolfocarrillo248 Thank you very much! :)

@anushreesaran Жыл бұрын

Got my copy of The StatQuest Illustrated Guide to Machine Learning today! Quadruple BAM!!!!

@statquest Жыл бұрын

@@anushreesaran Hooray! Thank you very much! :)

@tremaineification 8 ай бұрын

@@statquestwhat do mean by the last term not containing the intercept?

@moetasimrady8876 9 ай бұрын

I have started my machine learning journey a month ago and I stumbled onto a myriad of resources that explain linear models using the RSS function but no one, and I mean no one, managed to explain it with as much clarity and elegance as you have in just under 20 minutes. You sir are a boon to the world.

@statquest 9 ай бұрын

Thank you!

@pperez1224 3 жыл бұрын

Amazing pedagogy. Slow pace , short setences , visuals consistent with the talk. great job ;-) Thanks

@statquest 3 жыл бұрын

Glad you liked it!

@revolution77N 4 жыл бұрын

Man you are amazing. You should get a Nobel prize!

@statquest 4 жыл бұрын

Thank you! :)

@marcus2441 2 жыл бұрын

Agree!

@mammamiachemale 2 жыл бұрын

more than a nobel! book bought

@egyptianplanner Жыл бұрын

Yes Yes Yes

@afmartins666 Жыл бұрын

Or a Grammy!

@diyanair158 Жыл бұрын

Did I just UNDERSTAND the CHAIN RULE ? SURREAL, thank you!

@statquest Жыл бұрын

@ivanferreira5042 4 жыл бұрын

Nobody: The demon in my room at 3am: 7:56

@statquest 4 жыл бұрын

Dang! :)

@borisdjakovic 4 жыл бұрын

jesus, this was funny xD

@Ruostesieni Жыл бұрын

As someone who is doing medical research and needs to learn little-by-little about statistics, neural networks and machine learning as my project goes on, your channel is a literal life-saver! It has been so hard to try to keep my M.D. stuff together with my PhD research all the while learning statistics, programming and neural network structures and machine learning. Trying to arrange courses from my uni to fit in with all the other stuff is simply impossible, so I've been left to my own devices and find a way to gain knowledge about said subjects and your channel has done just that. Your teaching is great and down-to-earth enough to be easily grasped, but you also delve deep into the subject after the initial baby steps, so the person watching isn't just left with "nice to know"-infobits. Love it! Keep up the great work!

@statquest Жыл бұрын

Thank you!

@TheGreatFilterPodcast 2 жыл бұрын

BY FAR the best explanation of the chain rule I have ever seen (and trust me - I've seen A LOT) You, sir, just earned yourself yet another well-deserved subscriber. F'n brilliant!!!

@statquest 2 жыл бұрын

Thank you very much!!! BAM! :)

@ayushbatra2471 Жыл бұрын

Over the past three years, I have been studying neural networks and delving into the world of coding. However, despite my best efforts, I struggled to grasp the true essence of this complex subject. That is until I stumbled upon your enlightening video. I cannot emphasize enough how much your video has helped me. It has shed light on the intricate aspects of neural networks, allowing me to comprehend the subject matter with greater clarity and depth. The way you presented the material was truly remarkable, and it made a profound impact on my understanding. What astounds me even more is that you provide such valuable content for free. It is a testament to your passion for educating and empowering individuals like myself. Your dedication to spreading knowledge and fostering learning is truly commendable. Thanks to your channel, I have been able to unlock the true essence of mathematics and its relationship with neural networks. The confidence and clarity I now have in this subject are invaluable to my personal and professional growth. Your video has been a game-changer for me, and I am grateful beyond words. Please continue your fantastic work and know that your efforts are deeply appreciated.

@statquest Жыл бұрын

Thank you very much! BAM! :)

@Alchemist10241 2 жыл бұрын

Awesome!! None of my math teachers in high school or collage never explained to me WHY chain rule works this way. but you explained it with a very simple example. I'm certain that from now on I'll never forget the chain rule formula. Thanks a million. 👌✔

@statquest 2 жыл бұрын

BAM! :)

@amanrastogi603 2 ай бұрын

I am Biostatistician, proclaiming that you are really a good teacher.

@statquest 2 ай бұрын

Thank you very much!

@dc_amp8843 Жыл бұрын

The way you link equations to visuals and show how everything is working along with the math at the SAME time. Beautiful, elegant, easy to follow.

@statquest Жыл бұрын

Wow, thank you!

@RealSlimShady7 4 жыл бұрын

Guess I will not be afraid of the ***THE CHAAAAAINNNN RULE*** Thank you, Josh! Always Waiting for your videos!

@statquest 4 жыл бұрын

Bam! :)

@user-ul2mw6fu2e Жыл бұрын

Best chain rule explanation i have ever seen.

@statquest Жыл бұрын

Thank you!

@RahulVerma-Jordan 29 күн бұрын

If I watched your videos during my college, my career trajectory would be totally different. BIG BAM!!!!

@statquest 28 күн бұрын

Thanks!

@varunparuchuri9544 3 жыл бұрын

dear @stat quest you must have come from heaven to save students from suffering's just unbeliable explanation

@statquest 3 жыл бұрын

Thank you! :)

@putririzqiyah6294 3 жыл бұрын

this channel was suggested by my professor, and i always watch the videos while doing a machine learning tasks. Big appreciate to you :D

@statquest 3 жыл бұрын

Cool, thanks!

@markbordelon1601 Ай бұрын

We could have had a "dreaded terminology alert" : "decomposition of functions". But even without it: this was a perfect explanation of the chain rule , with great practical examples. Bravo, Josh!

@statquest Ай бұрын

Thank you!

@rigobertomartell5029 Жыл бұрын

Josh you are a master in teaching, you make difficult topics so easy to understand which is really amazing. My mother language is not English but you explain so well and clear that I can understand everything. Congratulations Sir, please keep doing this job.

@statquest Жыл бұрын

Thank you very much! :)

@vnaveenkumar982 3 жыл бұрын

Take my words Josh you are the best teacher on the internet who teaches Statistics........ and the chain rule made me crazy.......... by your explanation.

@statquest 3 жыл бұрын

Wow, thanks!

@vnaveenkumar982 3 жыл бұрын

@@statquest ❤️

@behrampatel3563 2 ай бұрын

This one outdoes all the best videos on the topic .

@statquest 2 ай бұрын

Thank you!

@nick_g Жыл бұрын

I love StatQuest! I got my SQ mug in the morning and just got the Illustrated Guide to Machine Learning. Super excited to start! Thank you for all the great content!

@statquest Жыл бұрын

That is awesome! TRIPLE BAM!!!! :)

@mr.shroom4280 Жыл бұрын

Bro your the only tutorial that actually helped me grasp this concept, thank you so much.

@statquest Жыл бұрын

Glad it helped!

@mr.shroom4280 Жыл бұрын

@@statquestI know this isn't related to this video, i just want you to help me because you replied to this comment. With gradeint descent, how am i supposed to get the derivative for each weight and bias in a loss function dynamically? because surely for networks with more than 100 neurons there would be a way, i know there is i just don't know. When i am calculating the derivative for one varaible in the loss function, to optimize it, i get some overly complicated function, but i see some papers on it and it isn't complicated.

@statquest Жыл бұрын

@@mr.shroom4280 See: kzfaq.info/get/bejne/f7Rii9Bzza-wpGg.html kzfaq.info/get/bejne/n9-eZd2VprLNmWw.html and kzfaq.info/get/bejne/fbGKorJ5va3HfKM.html

@mr.shroom4280 Жыл бұрын

@@statquest thankyou so much, i watched those but i totally forgot about the chain rule lol

@darshuetube Жыл бұрын

you have great videos that help explain a lot of concepts very clearly, step by step. You have help a lot of students for sure.

@statquest Жыл бұрын

Thank you very much! :)

@louco2 Жыл бұрын

This is probably the best video about on the internet!! Thank you so much for taking the time to do it!!

@statquest Жыл бұрын

Glad it was helpful!

@sheilawang3847 3 жыл бұрын

such a clean and simple explanation! can't wait for more Math and Statistic videos. You are the awesomeness in KZfaq!

@statquest 3 жыл бұрын

Thank you! :)

@jbboyne Жыл бұрын

Your videos are fantastic, even without the sound effects... but the sound effects really bring them over the top.

@statquest Жыл бұрын

Thank you! And thank yo so much for supporting StatQuest!!! BAM! :)

@ShermanSitter 4 жыл бұрын

I would insert a BAM at 5:25. :) ...also, I realized the thing I like about your videos is you explain things, not only in a clear way, but in a different way. It adds to the depth of our understanding. Thank you!

@statquest 4 жыл бұрын

That is definitely a BAM moment! And thank you. One of my goals is to always explain things in a different way, so I'm glad you noticed! :)

@gabrielcournelle3055 3 жыл бұрын

Now I can't read "the chain rule" without hearing your voice !

@statquest 3 жыл бұрын

@jhfoleiss 4 жыл бұрын

Awesome Explanation Mr. Starmer! I wish your videos existed back when I was taking Calculus in the university!!! ( which was a long time ago =) )

@statquest 4 жыл бұрын

Wow, thanks!

@anashaat95 Жыл бұрын

Very clear explanation. I saw different people explaining this topic but you are the best. Thank you so much.

@statquest Жыл бұрын

Thank you!

@robelbelay4065 3 жыл бұрын

An epically clear explanation. Thank you so much!

@statquest 3 жыл бұрын

Thank you! :)

@suneel8480 3 жыл бұрын

You had made my machine learning path easy!

@statquest 3 жыл бұрын

Glad to hear that!

@meow-mi333 4 ай бұрын

This dude explains things clearly. Huge thanks!

@statquest 4 ай бұрын

Thanks!

@dhakalsandeep3452 Жыл бұрын

One of the best video i have ever watched. Thank yoy guys for providing such a wonderful content for free.

@statquest Жыл бұрын

Thanks!

@prydt 8 ай бұрын

These seriously are some of my favorite videos on youtube!

@statquest 8 ай бұрын

Thanks!

@KUMAWANI 2 жыл бұрын

I would like to thank you from bottom of my heart for such wonderful videos. Such difficult topic made simple, you are awesome man , keep rocking!!!!

@KUMAWANI 2 жыл бұрын

And Triple BAM!!!!

@statquest 2 жыл бұрын

Thank you very much! :)

@joeyshias Жыл бұрын

i'm so moved to finally understand this, thank you!

@statquest Жыл бұрын

bam! :)

@harisjoseph117 2 жыл бұрын

Dear Josh Starmer, Thank you so much. May God bless with you more knowledge so that you can energize learners like me. ❤. Thank you again.

@statquest 2 жыл бұрын

Thank you very much!

@chelsie292 3 жыл бұрын

this is epic, simple, and applicable chain rule in real life too - we need more videos like this damn

@statquest 3 жыл бұрын

Thank you! :)

@MrXiiaoSky 2 жыл бұрын

thanks for clearing up the confusions i had with chain rule!

@statquest 2 жыл бұрын

bam!

@Vanadium404 11 ай бұрын

Such a beautiful intuition that weight height then height shoe size example was just commendable

@statquest 11 ай бұрын

Thanks!

@salah6160 7 ай бұрын

Teaching is an art. thank you StatQuest

@statquest 7 ай бұрын

Thank you!

@taiman9423 2 жыл бұрын

Top notch visualization.

@statquest 2 жыл бұрын

Thank you! :)

@vaishnavi4354 4 жыл бұрын

Awesome Statquest... Initially played Song and concept too!!😎😎😎

@statquest 4 жыл бұрын

Thanks! :)

@aswink112 3 жыл бұрын

Great teaching Josh Starmer!

@statquest 3 жыл бұрын

Thank you kindly!

@jialushen6248 4 жыл бұрын

Oh boy that's a teaser for neural net. Been looking forward to this!!

@statquest 4 жыл бұрын

YES!!! This is the first video in my series on Neural Nets!!!!!!! The next one should be out soon (hopefully late July, but I always run behind so maybe early August).

@saifqawasmeh9664 6 ай бұрын

Reading abour Loss in Neural Network and optimization from 20+ sources and could not understand it until watching this video. Big BAM!

@statquest 6 ай бұрын

Hooray! Thank you!

@ashwinkrishnan4285 3 жыл бұрын

Hey Josh You an awesome guy with amazing explanation of the concept through simple visuals. And this is my first video of yours. I got just amazed by the way you explained so simply. I would like to learn statistics, machine learning and deep learning as well. could u suggest me the order I have to walk through your playlist to get deep dive into those concepts with strong base. And keep up the good work. Cheers:)

@statquest 3 жыл бұрын

I have all my videos organized by topic and, within each topic, from simple to complicated here: statquest.org/video-index/

@tagoreji2143 Жыл бұрын

Thank you Sir for the amazing Tutorial.

@statquest Жыл бұрын

Thanks!

@luis96xd Жыл бұрын

Amazing video! Back to basics 😄👍

@statquest Жыл бұрын

Thanks!

@tanubist7721 3 жыл бұрын

This be the first time I am laughing learning stats🤣 Thanks alot!

@statquest 3 жыл бұрын

Hooray! :)

@favor2012able 3 жыл бұрын

Yet another bravo tutorial video! Thank you, Josh! One question is: what visual software/tool do you use to draw those beautiful plots? Are u like 3Blue1Brown to write a JS front-end tool yourself? Thanks!

@statquest 3 жыл бұрын

I'm glad you like the videos! I draw the pictures in Keynote.

@Adhithya2003 2 жыл бұрын

3b1b does not use JS front end tool , It's Python animation lib powered by Cairo (C lib) or now it uses Open GL.

@bozok1903 6 ай бұрын

Bam! You are awesome. Thanks a lot.

@statquest 6 ай бұрын

bam! :)

@amerjabar7825 2 жыл бұрын

The best video in the internet about the Chain Rule!

@statquest 2 жыл бұрын

Thank you!

@lin1450 3 жыл бұрын

Thank you so much for your videos! I got a StatQuest Shirt for my Birthday... hurray! :)

@statquest 3 жыл бұрын

BAM! :)

@victorialeigh2726 2 жыл бұрын

Hi Josh, thank you for your awesome video as always! Been learning with you for some time now. I really enjoy learning thru your lens, and been curious why you call terminology dreadful :D ? Although the first time exposure is always not easy, terminology is an anchor to me. It keeps me from getting adrift amidst the sea of confusing concepts and ideas. Sometimes teachers and tutors go so fast, so I make sure to ask them if what they are talking about has a name. So I can always read more about it at my pace when I'm lost again. Sharing a bit of my lens. Thank you always ;-) !

@statquest 2 жыл бұрын

I'm glad my videos are helpful and thank you for sharing your learning perspective with me.

@georgetzimas6882 2 жыл бұрын

13:15 Is the residual(squared) graph mirrored? Since residual=(observed - predicted), wouldn't that mean that when on the original graph the intercept is zero, the residual would be positive(2-1=1), so the position on the residual(squared) graph should be on the positive x-axis(x=1), as opposed to the negative side on the video, and vice versa?

@statquest 2 жыл бұрын

Yes! You are correct. Oops!

@pooravkadiyan 2 жыл бұрын

Your explanation is awesome. Make more videos.

@statquest 2 жыл бұрын

Thank you!

@nishantgoel3065 2 жыл бұрын

awsome work man!!!! you have created the best content...... I wish that you should be teaching us at our college🥺

@statquest 2 жыл бұрын

Thank you so much 😀

@dkutagulla 11 ай бұрын

Simply the best explanation of chain rule! Now I understand CR better to teach my kid when she needs it... Thank you!!! Do you publish a book on calculus I would love to buy it!

@statquest 11 ай бұрын

Thanks! I don't have a book on calculus, but I have on on machine learning: statquest.org/statquest-store/

@studgaming6160 Жыл бұрын

Thanks for informative video.

@statquest Жыл бұрын

Thanks!

@elielberra2867 Жыл бұрын

Amazing video thanks!

@statquest Жыл бұрын

Thanks!

@alinadi9427 3 ай бұрын

your videos are fantastic

@statquest 3 ай бұрын

Glad you like them!

@orrlevinger 3 жыл бұрын

LOVE YOUR CONTENT BEST FUN LEARNING EVER!!! (The chain rule is COOL)

@statquest 3 жыл бұрын

bam!

@hassanalimohammadi4553 2 жыл бұрын

hanks for all your amazing videos. I'm still learning from you :)

@statquest 2 жыл бұрын

Thank you!

@_coderizon 2 ай бұрын

Thank you!!!

@statquest 2 ай бұрын

bam! :)

@valor36az 4 жыл бұрын

Awesome. You made my day!

@statquest 4 жыл бұрын

Hooray! :)

@warrenb7450 4 жыл бұрын

The best Chain Role tutorial! Do you have any for Relu? Thank you!!

@statquest 4 жыл бұрын

Coming soon!

@gojo8627 Жыл бұрын

BAM! best explanation so far

@statquest Жыл бұрын

Thank you! :)

@hakulab920 2 жыл бұрын

I'm getting gradually waiting for the "BAM".....I've been addicted to it....

@statquest 2 жыл бұрын

bam! :)

@janscheuring2642 Жыл бұрын

Hi, I think I found a mistake. (?) The pink ball in the graph from 13:08 should be on the other side of the Y axis. It doesn't change the educational value of the whole video but it caught my eye.

@janscheuring2642 Жыл бұрын

Oh, I see someone already brought this up.

@statquest Жыл бұрын

yep

@edphi 2 жыл бұрын

Genius serious sincere I’m a mathematician and am convinced you are a born sage

@statquest 2 жыл бұрын

Thanks!

@mattaaron79 Жыл бұрын

I'm getting strong MST3K and Star Control II vibes from this guy and that's pretty cool

@statquest Жыл бұрын

bam!

@aleksandrpakhomov4154 7 ай бұрын

Спасибо, вы молодец!

@statquest 7 ай бұрын

bam! :)

@tymothylim6550 2 жыл бұрын

Wow what a great video! Thanks a lot :)

@statquest 2 жыл бұрын

Glad you liked it!

@alfcnz 3 жыл бұрын

6:52 that's not an exponential line (2^x), it's just a parabola (x^2). Anyhow, you're awesome! BAM! Just subscribed!

@statquest 3 жыл бұрын

Thanks for catching that. :)

@dhruvsharma7992 2 жыл бұрын

This video is not just the explanation of "The Chain Rule" instead explained the intuition behind the various loss functions.

@statquest 2 жыл бұрын

That's right. The chain rule is used a lot in machine learning so I tried to explain it from that perspective.

@dhruvsharma7992 2 жыл бұрын

@@statquest Thanks for all of the videos, they all really help alot

@statquest 2 жыл бұрын

@@dhruvsharma7992 Thanks!

@ukkyukang 29 күн бұрын

Thanks!

@statquest 29 күн бұрын

bam! :)

@irischin6165 Жыл бұрын

I graduated with stats degrees from college 10+ years ago and never touched it. Now I feel I re-learned everything overnight!!!!!

@statquest Жыл бұрын

BAM! :)

@Infinitesap Жыл бұрын

I think you must be an alien! This is the best, most simplistic and complete explanation I have seen -ever. Fantastic job you did ❤️ thanks

@statquest Жыл бұрын

Thank you!

@supernenechi 9 ай бұрын

Despite how good you are at explaining, I'm still having a hard time with it all. My confidence isn't exactly helped by the fact that all the other people in the comments seem to somehow be doing PhDs and stuff, but okay... How can I try to understand it even better?

@statquest 9 ай бұрын

Can you tell me what time point, minutes and seconds, you first got confused?

@bob_bobsen 2 жыл бұрын

The graph at the start made me crack up. Deadpan humour >>>>>

@statquest 2 жыл бұрын

@KayYesYouTuber 2 жыл бұрын

Simply beautiful. you are the best.

@statquest 2 жыл бұрын

Wow, thank you!

@user-or7ji5hv8y 4 жыл бұрын

A video also on probability chain rule would be awesome

@statquest 4 жыл бұрын

Noted! :)

@ge13r Ай бұрын

Saludos desde la UNET

@statquest Ай бұрын

@Metryk 10 ай бұрын

13:27 When the residual is negative, the pink circle is shown to be on the right side of the y-Axis, but shouldn't it be on the left side? Aside from that, great content! Cheers from Germany

@statquest 10 ай бұрын

Yep. Thanks for catching that! I've added a correction to the pinned comment.

@Vinyl-vv3pz 11 ай бұрын

Best reference for learning statistics. Btw, would just like to point out that in 6:16, there appears to be a minor mistake. Actually for every 1 unit increase in Weight, there is a 2 unit increase in Shoe Size, because the equation would be Size = (1/2)*Weight, or 2*Size = 1*Weight

@statquest 11 ай бұрын

This video is actually correct. For every one unit increase in weight, there is only a 1/2 unit increase in Shoe Size. What your equation shows is that for every unit increase in Size, there is a 2 unit increase Weight. That's not the same thing as "for every unit increase in Weight, there is a 2 unit increase in Size".

@Vinyl-vv3pz 11 ай бұрын

@@statquest I calculated through the equation, and you are correct. Thanks for the verification!

@birzhanabdikhan45 2 жыл бұрын

There are people who love StatQuest and there are people who don't know about StatQuest yet... poor souls

@statquest 2 жыл бұрын

Thanks! :)

@wrjazziel 3 жыл бұрын

LMAO, the song at the beginning xD, just for that I'm giving it a like.

@statquest 3 жыл бұрын

BAM! :)

@jn7457 4 жыл бұрын

Thank you!

@statquest 4 жыл бұрын

Thanks! :)

@siddean5048 Жыл бұрын

Beautiful Just Beautiful

@statquest Жыл бұрын

Thank you! 😊

@duydangdroid 11 ай бұрын

3:00 should be a BAM!! within another BAM!! by The Chain Rule

@statquest 11 ай бұрын

Yes! :)

@motherisape 2 жыл бұрын

Awesomeness = like statquest squared 😆 🤣

@statquest 2 жыл бұрын

Thank you!

@akistsili8574 Жыл бұрын

Really....you are amazing!

@statquest Жыл бұрын

Thank you so much 😀

@zhipengluo5831 3 жыл бұрын

So good !!!!

@statquest 3 жыл бұрын

Thank you! :)

@shixianxu2994 Жыл бұрын

Awesome!

@statquest Жыл бұрын

Thanks!

@tillsch1 3 жыл бұрын

Amazing Video. Helps a lot! Does anyone know an example of an empirical research paper in which the chain rule (two step procedure) is applied in the context of empirical testing of the research question/hypothesis? Thank you very much for a reply!

@statquest 3 жыл бұрын

Logistic Regression uses Gradient Descent, which, in turn, often uses the chain rule

@tillsch1 3 жыл бұрын

@@statquest Dear Josh, thank you for your answer. I want to concretise my question. I understood from your videos that the chain rule is used in neural networks to solve the optimization problem and also in logistic regression using gradient descent etc.. I'm currently looking for a content example of published research (= a concret study) in which the modelling approach weight (some indepedent variable) predicts height(some other independent variable) and height predicts shoe size(dependent variable). Does anyone know an example of such an empirical research paper? Thank you very much for a reply!