Support Vector Machines Part 3: The Radial (RBF) Kernel (Part 3 of 3)
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- Опубліковано 3 лис 2019
- 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...
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You make statistics and machine learning so much fun. Your channel is binge watch worthy. Keep spreading good education in fun way. :)
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@@philipkopylov3058 psst, in a flat affine subspace of dimension 2
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@@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
@@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
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.
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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 :)
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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!
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.
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 !
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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!
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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.
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What an interesting application of the Taylor Series. Such a beautiful explanation, thank you!
This is actually the 3rd place I've seen the Taylor Series in Machine Learning - so it's a super useful trick.
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Awesome!!! I'm glad my video was helpful. :)
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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.
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the relationship between two objects in infinite dimension.
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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.
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OK got what diamension relationship means now. You the best
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Thanks!
Can’t believe I used my knowledge on Taylor series expansion. Thanks for not wasting precious brain space for that
BAM! The Taylor series actually pops up a bunch in machine learning (Gradient Boost and XGBoost etc.)
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@Eyal Barazan I would recommend starting with the first video in this series: ua-cam.com/video/efR1C6CvhmE/v-deo.html
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Could you please explain how UMAP works? Also, comparison UMAP with tSNE will be nice )
UMAP is on the to-do list.
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Glad you enjoyed it!
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
Thank you!
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?
Well explained
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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.
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
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I learned RBF from the Gaussian process, and seems the idea of "kernal" has numerous applications!
Yes!
Thanks for the amazing video. Just one quick question. When calculating the relationship between two observations, the larger the distance between the two observations, the smaller the high-dimensional relationship results. You says it is because there is less influence between the two. But, as in the example, the observations (red) are spreading on the both sides of the green observations, while they are in the same classification. According to the distance rule mentioned above, the high-dimensional relationships results between the two red observations ,laying separately on the both side of the green observation, will also be very small. How to explain the weak relationship between observations in the same classification? Is that also because of weaker influence?
It's OK for two items from the same category to have a low value. The goal is to find a linear classifier in a high dimensional space that separates the two categories. If that means we have multiple clusters that represent the same category, that is OK as long as we can separate them from the other category.
Just can't wait for more svm's
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.
@@statquest When are you planning to upload XGBoost Video, your videos are awesome!!
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.
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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)
Even i do have the same doubt on how the relationship is used further in classification.. please help
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?
We can always use 10-fold cross validation to compare how different models perform: ua-cam.com/video/fSytzGwwBVw/v-deo.html