Support Vector Machines Part 3: The Radial (RBF) Kernel (Part 3 of 3)

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StatQuest with Josh Starmer

StatQuest with Josh Starmer

4 роки тому

Support Vector Machines use kernel functions to do all the hard work and this StatQuest dives deep into one of the most popular: The Radial (RBF) Kernel. We talk about the parameter values, how they calculate high-dimensional coordinates and then we'll figure out, step-by-step, how the Radial Kernel works in infinite dimensions.
NOTE: This StatQuest assumes you already know about...
Support Vector Machines: • Support Vector Machine...
Cross Validation: • Machine Learning Funda...
The Polynomial Kernel: • Support Vector Machine...
ALSO NOTE: This StatQuest is based on...
1) The description of Kernel Functions, and associated concepts on pages 352 to 353 of the Introduction to Statistical Learning in R: faculty.marshall.usc.edu/garet...
2) The derivation of the of the infinite dot product is based on Matthew Bernstein's notes: pages.cs.wisc.edu/~matthewb/pa...
For a complete index of all the StatQuest videos, check out:
statquest.org/video-index/
If you'd like to support StatQuest, please consider...
Buying The StatQuest Illustrated Guide to Machine Learning!!!
PDF - statquest.gumroad.com/l/wvtmc
Paperback - www.amazon.com/dp/B09ZCKR4H6
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Patreon: / statquest
...or...
UKposts Membership: / @statquest
...a cool StatQuest t-shirt or sweatshirt:
shop.spreadshirt.com/statques...
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joshuastarmer.bandcamp.com/
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www.paypal.me/statquest
Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter:
/ joshuastarmer
#statquest #SVM #RBF

КОМЕНТАРІ: 591
@statquest
@statquest 2 роки тому
Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/
@hawaiicashew3237
@hawaiicashew3237 Місяць тому
Holly cow this one is flying high. The guy who figured out all the maths must have been on fire!
@statquest
@statquest Місяць тому
bam!
@priyangkumarpatel9317
@priyangkumarpatel9317 3 роки тому
You make statistics and machine learning so much fun. Your channel is binge watch worthy. Keep spreading good education in fun way. :)
@statquest
@statquest 3 роки тому
Wow, thanks
@chemgreec
@chemgreec 3 роки тому
Excellent! There is a higher dimensional space where this video is linearly seperable from anything else on youtube. What I love is that you use both math and intuition in good measure. You dont sacrifice intutition over math or math over intuition like most other attempts. This balance you ve got here is excellent.
@statquest
@statquest 3 роки тому
Wow, thank you!
@RM-zx9ee
@RM-zx9ee 2 роки тому
This video deserves an Oscar. Seriously, that was incredible. Infinite BAM!
@statquest
@statquest 2 роки тому
Thanks! BAM! :)
@ayoubmarah4063
@ayoubmarah4063 4 роки тому
i bet there is a place in heaven named statquest where you gonna live an internal life there
@statquest
@statquest 4 роки тому
Thank you very much!!!! :)
@philipkopylov3058
@philipkopylov3058 3 роки тому
* a place between heaven and earth with the biggest margin possible
@bnglr
@bnglr Рік тому
@@philipkopylov3058 psst, in a flat affine subspace of dimension 2
@kk___kk___kk
@kk___kk___kk Рік тому
I find some beep boop sounds a bit cringe, but it's crazy how good you are at explaining and showing things step-by-step. Thank you so much !
@statquest
@statquest Рік тому
bam! :)
@EtherealMetal
@EtherealMetal 4 роки тому
This channel is so amazing。For the past few months I have been trying to catch up on concepts in statistics that my university never taught so that I have enough knowledge to go into the data science and machine learning fields。 The way you teach concepts in clear concise and short videos is extremely valuable。I have learned much in such a short time from just watching your videos and taking handwritten notesーthank you for all the hard work you have put in delivering this invaluable knowledge!Please continue making videos!
@statquest
@statquest 4 роки тому
Thank you very much! :)
@arunavsaikia2678
@arunavsaikia2678 4 роки тому
@@statquest Hey Josh, what would be an intuitive way to understand how SVM uses the high dimensional relationship between each pair of points to make the actual classification
@statquest
@statquest 4 роки тому
@@arunavsaikia2678 This is a good question. The dot product between two points, which we use to create the "high-dimensional relationships," can be interpreted in a geometric way that includes the cosine of the angle between the two points multiplied by their magnitudes (the distances from the origin). With that in mind, check out slide 18 in this PDF: web.mit.edu/6.034/wwwbob/svm.pdf
@Illinoise888
@Illinoise888 4 роки тому
My university skimmed over RBF, but then had 15 marker about it on the midterm.. Now studying for finals, and wish I had this video for the midterm.
@This_isNotAThing
@This_isNotAThing 3 роки тому
Yes please
@SometimesMagii
@SometimesMagii Рік тому
the mathematical reasoning behind the radial kernel has been plaguing me for so long, finally after many tries now it starts to click and my mind can visualize better what is happening and why. Thank you so much :)
@statquest
@statquest Рік тому
Bam!
@yulinsun8873
@yulinsun8873 2 роки тому
Infinite Bam! This is the most understandable ML video I ever watched. Thank you for sharing this.
@statquest
@statquest 2 роки тому
Glad it was helpful!
@akrylic_
@akrylic_ 4 роки тому
What an interesting application of the Taylor Series. Such a beautiful explanation, thank you!
@statquest
@statquest 4 роки тому
This is actually the 3rd place I've seen the Taylor Series in Machine Learning - so it's a super useful trick.
@kartikbhanot4692
@kartikbhanot4692 3 роки тому
I was finding it hard to understand the concept of RBF and this video helped me immensely. Thank you Josh for the amazing work that you doing.
@statquest
@statquest 3 роки тому
Thank you very much! :)
@richf.9211
@richf.9211 26 днів тому
This man just answered questions I didn’t even know I had!😂 Excellent job thank you for the videos!
@statquest
@statquest 26 днів тому
Happy to help!
@mypure
@mypure 2 роки тому
Watching Josh is like feeling like Flash of statistical concepts.. Every skipped concepts in stat class seems becoming crystal clear here..
@statquest
@statquest 2 роки тому
bam! :)
@hoangtrunghaipham5999
@hoangtrunghaipham5999 4 роки тому
I have gone through 85% of the full list and found this series extremely useful. The instructions are simple to understand and give the sufficient overview into Machine learning. Highly recommend for starters like me. Looking forward to the advanced parts, e.g. Deep learning. Many thanks!
@statquest
@statquest 4 роки тому
SVM and the Radial is actually pretty advanced, so you've made huge progress. The current series, on XGBoost, is also very advanced. After this, I'll do deep learning and neural networks.
@jeongwonkim247
@jeongwonkim247 4 роки тому
The best machine learning statistics video. Came from confused at a coursera course for data science, taught by u mich faculty, and this video does that 100000x better. Thank you so much!
@statquest
@statquest 4 роки тому
Awesome!!! I'm glad my video was helpful. :)
@lauriesteveescoses590
@lauriesteveescoses590 13 днів тому
holy shit, i didnt expect series expansion to come at the end. so cool
@statquest
@statquest 12 днів тому
bam! :)
@sinkseeker
@sinkseeker 7 місяців тому
The way you explain the math is astounding! I hope you'll continue making videos like this!
@statquest
@statquest 7 місяців тому
Thanks, will do!
@clapdrix72
@clapdrix72 4 роки тому
One of the most clearly explained proofs I've seen in a while
@statquest
@statquest 4 роки тому
Thank you very much! :)
@nabeelhasan6593
@nabeelhasan6593 3 роки тому
Your videos are like magic, making such a difficult derivation look so much easy. God Bless You
@statquest
@statquest 3 роки тому
Thanks a lot 😊!
@dome8116
@dome8116 4 роки тому
Thanks for creating this amazing video. After watching the lecture on RBF from Caltech I was so lost and felt so bad since it was the first concept that I didnt understand at all. Your video gave some good intuition why it works and how. Thank you Statquest :D
@statquest
@statquest 4 роки тому
Awesome! :)
@tonysand69
@tonysand69 3 роки тому
Oh man, thanks you for your videos, i mean, you're really awesome. You don't only explain the concepts, but also you keep it real and fun. I have learned a lot from you, when i have money i will donate every penny of it.
@statquest
@statquest 3 роки тому
Wow, thanks!
@hashiska.5358
@hashiska.5358 4 роки тому
nobody explains the concepts better than you do. I have to study ML for a project and I haven't found a channel better than yours. That is why I have a request: please make a video on Support Vector Regression.
@tampopo_yukki
@tampopo_yukki 9 місяців тому
When I was struggling to understand what the use of kernel is intuitively, I found this video in StatQuest series. Now, this seems to have fixed my shaky comprehension about the kernel! Your video series are one of my favorite explanations for base of ML. I'm so glad if you'd keep making these kinds of interesting videos on your pace, BAM!
@statquest
@statquest 9 місяців тому
Thank you very much! :)
@skelgamingyt
@skelgamingyt 5 місяців тому
Please take our professor's job. We need you.
@statquest
@statquest 5 місяців тому
:)
@trenton7
@trenton7 2 роки тому
The initial singing and the double, triple, quadruple bam grows on you, didn't like them much at first but it is now an essential part of the learning experience for me.
@statquest
@statquest 2 роки тому
bam
@gautamdawar5067
@gautamdawar5067 3 роки тому
A beautiful video, I had tears of joy after watching this. Sir you are amazing!
@statquest
@statquest 3 роки тому
Wow, thank you!
@tanmaymehta9696
@tanmaymehta9696 Рік тому
Thank you so much for making all these ML and stats terms so understandable! Great work!
@statquest
@statquest Рік тому
My pleasure!
@ketkiambekar7607
@ketkiambekar7607 3 роки тому
Thank you for making one of the best videos out there for understanding SVM (and log likelihood maximization, and countless other concepts). I am going to make a good contribution to your Patreon once I get start earning because you so so deserve it, omigosh.
@ketkiambekar7607
@ketkiambekar7607 3 роки тому
nananananananana StatQuest!
@statquest
@statquest 3 роки тому
Thank you very much! :)
@mustufakerawala1796
@mustufakerawala1796 4 роки тому
I love your videos!!! I understand this content better, even better than my data science lecture at uni. I hope you keep up the great work, I'm officially gonna get some Statquest merch to support this chanel.
@statquest
@statquest 4 роки тому
Awesome! :)
@xlmentx
@xlmentx 3 роки тому
Damn, good job dude. At first I felt like I was being talked down to, but eventually grew to like it lol. You're way better at teaching this stuff than my professor is.
@statquest
@statquest 3 роки тому
Glad you like it. I try to teach the way I want to be taught myself. I'm not super good at this stuff, so I try to keep it simple.
@wangwenyu9052
@wangwenyu9052 4 роки тому
Thanks for the wonderful video! It really helps in both forming the intuitive, as well as connecting key math concept together!
@statquest
@statquest 4 роки тому
Thanks! :)
@yuqing3667
@yuqing3667 2 роки тому
Now we can eat snacks! Thank you so much, your visual explanation makes things so much easier to understand.
@statquest
@statquest 2 роки тому
Glad it was helpful!
@prashant4814
@prashant4814 4 роки тому
wow, god bless you we need good teachers like you
@statquest
@statquest 4 роки тому
Thank you very much! :)
@user-ee3qt2fb7i
@user-ee3qt2fb7i Рік тому
Every time I watch your visualized explanation, I just got amazed
@statquest
@statquest Рік тому
Thank you!
@fatihboyar9697
@fatihboyar9697 10 місяців тому
calculation noises are so realistic and horizon widening experience
@statquest
@statquest 10 місяців тому
BAM!
@jiayiwu4101
@jiayiwu4101 3 роки тому
Such a nice, crystal, clear explanation!! Awesome job!!!
@statquest
@statquest 3 роки тому
:)
@andersoneduardo749
@andersoneduardo749 Рік тому
you are the best math professor I ever had.. thanks a lot!!
@statquest
@statquest Рік тому
Wow, thanks!
@devindoinmonkmode
@devindoinmonkmode 7 місяців тому
3hours lectures in 15 mins, and it's super funny. Super Bam for StatQuest
@statquest
@statquest 6 місяців тому
Thanks!
@akashjain35
@akashjain35 4 роки тому
This video and in fact the whole playlist of machine learning is so amazing. Your way of teaching makes it so easy to understand the mathematics behind these concepts. Don't ever stop making these videos!
@statquest
@statquest 4 роки тому
Thank you very much!!!! :)
@KiranDhakal8848
@KiranDhakal8848 21 день тому
As I continue watching your video the satisfaction of understanding BAMSS EXPONENTIALLLY!!!
@statquest
@statquest 21 день тому
:)
@ilyabykov2437
@ilyabykov2437 Рік тому
If I ever get a job in data science, it'll be thanks to this guy.
@statquest
@statquest Рік тому
bam! :)
@cheshtagupta7491
@cheshtagupta7491 3 роки тому
this video put an instant smile on my face
@statquest
@statquest 3 роки тому
Wow, thank you!
@jasonfaustino8815
@jasonfaustino8815 2 роки тому
Can’t believe I used my knowledge on Taylor series expansion. Thanks for not wasting precious brain space for that
@statquest
@statquest 2 роки тому
BAM! The Taylor series actually pops up a bunch in machine learning (Gradient Boost and XGBoost etc.)
@user-zy8sf7tv2f
@user-zy8sf7tv2f 2 роки тому
Hey man, I have to thank you a lot for describing these things so well ! Thank you very much !
@statquest
@statquest 2 роки тому
Thank you!
@winstonzhang6352
@winstonzhang6352 2 роки тому
Amazing video, this saved me for my ML midterm. THANK YOU.
@statquest
@statquest 2 роки тому
Glad it helped!
@tymothylim6550
@tymothylim6550 3 роки тому
Thank you very much for this video! I learnt a lot from this step-by-step math guide! Great to eat snacks too!
@statquest
@statquest 3 роки тому
Double bam! :)
@maverickop4134
@maverickop4134 3 роки тому
this explanation made it look too easy. Good job . Thanks for making this video.
@statquest
@statquest 3 роки тому
Thank you! :)
@MominSaadAltafnab
@MominSaadAltafnab Рік тому
"pipipu pipipu" hits every time 😂
@statquest
@statquest Рік тому
bam! :)
@abir95571
@abir95571 3 роки тому
Not gonna lie , I have read a few other books understanding how RBF computes relationship between data points in infinite dimension ... none of them are as simple and comprehensive as your video. Thanks a lot
@statquest
@statquest 3 роки тому
Thank you!
@ritshpatidar
@ritshpatidar 5 місяців тому
The guy who came up with RBF is genius.
@statquest
@statquest 5 місяців тому
yep
@RH-zp1ry
@RH-zp1ry 3 роки тому
15:18 I would say "INFINITE BAM!!!"
@statquest
@statquest 3 роки тому
YES!
@paulovinicius5833
@paulovinicius5833 3 роки тому
I was SO hoping for that to happen! hahaha I was expecting this part to be the largest BAM he ever did hahah
@statquest
@statquest 3 роки тому
@Eyal Barazan I would recommend starting with the first video in this series: ukposts.info/have/v-deo/nZaDZXlteqyZznk.html
@peterng.
@peterng. 11 місяців тому
worth to spend times on! thank you Josh!
@statquest
@statquest 11 місяців тому
Thank you!
@harithagayathri7185
@harithagayathri7185 4 роки тому
Very clear explanations and far better than the videos on udemy !!
@statquest
@statquest 4 роки тому
Thank you! :)
@shauryavatsa595
@shauryavatsa595 6 місяців тому
I wish I could be taught by you physically. I know nothing about machine learning and I am going through some of the topics for my internship and I cannot tell you how easy you are making things for me. Quadruple BAMM!!
@statquest
@statquest 6 місяців тому
Bam! I'm glad you enjoy the videos. :)
@sabrinapatania7810
@sabrinapatania7810 4 роки тому
Beautiful video! Thank you so much! I have a question. May you explain why we can use Taylor series assuming a=0? Why can we do this assumption?
@samyadeep906
@samyadeep906 4 роки тому
This was really good, thank you ♥️
@statquest
@statquest 4 роки тому
Thank you! :)
@umeshphadke6745
@umeshphadke6745 2 роки тому
This channel is absolute gold ! Thanks for your help mate , and also you should consider teaching mathematics too.
@statquest
@statquest 2 роки тому
I'll keep that in mind! :)
@muskankhajuria1038
@muskankhajuria1038 3 роки тому
Amazing teaching! Thank you sooo much!
@statquest
@statquest 3 роки тому
Glad it was helpful!
@feynmanc303
@feynmanc303 2 роки тому
thank you .. you make things super easy to understand.. amazingly good
@statquest
@statquest 2 роки тому
Thanks!
@mariafirulyova5020
@mariafirulyova5020 4 роки тому
Dear Josh Starmer, thanks for all amazing videos! Your channel is really helpful for me. Could you please explain how UMAP works? Also, comparison UMAP with tSNE will be nice )
@statquest
@statquest 4 роки тому
UMAP is on the to-do list.
@ahming123
@ahming123 4 роки тому
OK got what diamension relationship means now. You the best
@perstarke1295
@perstarke1295 3 роки тому
Wow. Just WOW. Hella good explanation!
@statquest
@statquest 3 роки тому
Glad you liked it!
@parthsharma8269
@parthsharma8269 Рік тому
What are you Josh? Clear - Done, Concise- Done, Amazing -Done, Infinite BAM!!
@statquest
@statquest Рік тому
HOORAY! :)
@jinyunghong
@jinyunghong 2 роки тому
This is such a great lecture!!
@statquest
@statquest 2 роки тому
Thanks! :)
@toxic_narcissist
@toxic_narcissist 3 роки тому
but how underrated is this video
@statquest
@statquest 3 роки тому
:)
@Hermioneswand1
@Hermioneswand1 2 роки тому
I love this channel. Much love! :)
@statquest
@statquest 2 роки тому
Thank you! :)
@henryatehortua6149
@henryatehortua6149 3 роки тому
I don't understand much English but I notice that you are a lot of fun teaching.
@statquest
@statquest 3 роки тому
Thank you very much! :)
@61_shivangbhardwaj46
@61_shivangbhardwaj46 2 роки тому
No words for you sir You are great!
@statquest
@statquest 2 роки тому
Bam! :)
@joxa6119
@joxa6119 2 роки тому
I just regret not found your channel during my degree.
@statquest
@statquest 2 роки тому
better late than never! :)
@boranzhou937
@boranzhou937 4 роки тому
thanks, man! this is really helpful!
@statquest
@statquest 4 роки тому
Thanks! :)
@sakshambali3040
@sakshambali3040 3 роки тому
Just amazing stuff man. God bless you, love from Indian..!!
@statquest
@statquest 3 роки тому
Thank you very much! :)
@buh357
@buh357 2 роки тому
wow wow wow, the relationship between two objects in infinite dimension. absolutely beautiful and amazing. thanks for ML and you :)
@statquest
@statquest 2 роки тому
Thanks!
@taotaotan5671
@taotaotan5671 2 роки тому
I learned RBF from the Gaussian process, and seems the idea of "kernal" has numerous applications!
@statquest
@statquest 2 роки тому
Yes!
@justgame5508
@justgame5508 3 роки тому
Ahhh thankyou electronic engineering for having difficult mathematics, it’s makes it easy to branch out into more statistical domains such as machine learning and still be able to keep up, also equips me with other techniques such as Fourier and Laplace transforms which can be useful in data analysis and feature extraction. Great derivation btw
@statquest
@statquest 3 роки тому
Thank you!
@filipfolkesson3865
@filipfolkesson3865 10 місяців тому
This was so funny and educational, thanks man
@statquest
@statquest 10 місяців тому
Thanks!
@siddharthpilli62
@siddharthpilli62 3 роки тому
I Love the videos you make keep up the good work!! BAM!!
@statquest
@statquest 3 роки тому
Thanks! Will do!
@amishgoel2377
@amishgoel2377 4 роки тому
Awesome Video and clear explanations! I had one doubt. In the end when forming dot product of RBF kernel, you have used s to multiply the two dot products. But s is a function of both a and b. In the dot product of a pair of observations in high dimension, each term in the product should be a function of one observation since it corresponds to high dimensional feature of an observation. I think one should multiply e^(-0.5a^2) to the first term and e^(-0.5b^2) to the second term of the dot product.
@statquest
@statquest 4 роки тому
All 's' is doing is scaling the dot-product by a constant value. For more details, see: pages.cs.wisc.edu/~matthewb/pages/notes/pdf/svms/RBFKernel.pdf
@kamran_desu
@kamran_desu 3 роки тому
Amazing explanation as always. Can you please also touch on the concept of "landmarks", how do they fit into this logic?
@statquest
@statquest 3 роки тому
I'll keep that topic in mind.
@williamobando4159
@williamobando4159 3 роки тому
This blew my mind lob u Josh ty
@statquest
@statquest 3 роки тому
Thanks!
@naufalamiruddin5798
@naufalamiruddin5798 2 роки тому
I love the "beep boop boop" part of this video !! 🤣
@statquest
@statquest 2 роки тому
:)
@himanshu1056
@himanshu1056 2 роки тому
Awesome explanation 👍
@statquest
@statquest 2 роки тому
Thanks!
@ManojGupta-tb3ei
@ManojGupta-tb3ei 6 місяців тому
Well explained Thank you....
@statquest
@statquest 6 місяців тому
Thanks!
@ashishtiwari1912
@ashishtiwari1912 4 роки тому
Thank you for the videos. i have learned a lot of things from your channel. What I would like to know is the scenarios where the SVM algorithm will fail. How do we make a relative comparison while choosing the different classification Algorithms?
@statquest
@statquest 4 роки тому
We can always use 10-fold cross validation to compare how different models perform: ukposts.info/have/v-deo/noOqqLB-rq1zt6s.html
@yavdhesh
@yavdhesh 4 роки тому
Namastey, you are the best person.
@statquest
@statquest 4 роки тому
Thank you! :)
@dougIas1
@dougIas1 2 роки тому
That's soo good :'). Thanks man!!!
@statquest
@statquest 2 роки тому
Glad you like it! :)
@harshitlamba155
@harshitlamba155 2 роки тому
You are Richard Feynman of this era!
@statquest
@statquest 2 роки тому
Thank you!
@well....7751
@well....7751 4 роки тому
I wanted to know what relationship do we get after doing the dot product between the values and can you do a video on support vector regression or give some links?? (Great video though)
@adarshs6571
@adarshs6571 3 роки тому
Even i do have the same doubt on how the relationship is used further in classification.. please help
@RanjeetSingh-pp4uu
@RanjeetSingh-pp4uu 3 роки тому
LOVED IT! THANKS!!
@statquest
@statquest 3 роки тому
Glad you enjoyed it!
@jeevanraajan3238
@jeevanraajan3238 4 роки тому
There is soo much of effort put into making these videos and it has come out soo welll !! When you die...You ll leave behind a legacy and will be known as a legend !!..
@statquest
@statquest 4 роки тому
Thank you very much! :)
@MsIHateMiley
@MsIHateMiley 3 роки тому
god bless, this channel is amazing
@statquest
@statquest 3 роки тому
Thank you! :)
@e555t66
@e555t66 Рік тому
Really explained well. If one wants to get the theoretical concepts one could try doing the MIT micromasters. It’s rigorous and demands 10 to 15 hours a week.
@statquest
@statquest Рік тому
bam!
@yafoniahutabarat6793
@yafoniahutabarat6793 2 роки тому
you should collab with Phoebe to create some StatQuest jingles!!!! love it
@statquest
@statquest 2 роки тому
:)
@caiochaves9550
@caiochaves9550 Місяць тому
Amazing!
@statquest
@statquest Місяць тому
Thank you!
@wolfisraging
@wolfisraging 4 роки тому
Just can't wait for more svm's
@statquest
@statquest 4 роки тому
Unfortunately, my next series of videos will be on XGBoost. If there if there is a demand, I'll return to SVMs as soon as I can.
@gauravgogia9939
@gauravgogia9939 4 роки тому
@@statquest When are you planning to upload XGBoost Video, your videos are awesome!!
@statquest
@statquest 4 роки тому
XGBoost videos should start coming out in the next few weeks. The first step is to learn how regression trees are traditionally pruned. XGBoost uses a different method and we need to learn the traditional way to appreciate how XGBoost does it.
@hustler212
@hustler212 2 роки тому
You're a life saver.
@statquest
@statquest 2 роки тому
bam!
@haochang4293
@haochang4293 4 роки тому
I benefit so much from your video. From a Chinese Ph.D.
@statquest
@statquest 4 роки тому
Awesome! :)
@ganesha.k.s
@ganesha.k.s 4 роки тому
Thanks a lot bro. This saved me
@statquest
@statquest 4 роки тому
Awesome! :)
@prajwalbandekar3557
@prajwalbandekar3557 4 роки тому
@@statquest The dude got 37/40 in his tests!
@statquest
@statquest 4 роки тому
@@prajwalbandekar3557 That is totally awesome!!!! :)
@xuemeiwang1881
@xuemeiwang1881 3 роки тому
GREAT MAN, GREAT CHANNEL.
@statquest
@statquest 3 роки тому
Thank you so much 👍
@vncoolestguy
@vncoolestguy 4 місяці тому
+ 3 views, thanks for awesome tutorials Josh.
@statquest
@statquest 4 місяці тому
Thanks!
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