This is showing that the quality and value of a video is not depending on how fancy the animations are, but how expert and pedagogue the speaker is. Really brilliant! I assume you spent a lot of time designing that course, so thank you for this!
"Now that we understand the REASON we're doing this, let's get into the math." The world would be a better place if more abstract math concepts were approached this way, thank you.
This is awesome! Lots of machine learning books or online courses don't bother explaining the reason behind Ridge regression, you helped me a lot by pulling out the algebraic and linear algebra proofs to show the reason WHY IT IS THIS! Thanks!
I was searching for ridge regression on the whole internet and stumbled upon this is a video which is by far the best explanation you can find anywhere thanks.
Excellent video! One more thing to add - if you're primarily interested in causal inference, like estimating the effect of daily exercise on blood pressure while controlling for other variables, then you want an unbiased estimate of the exercise coefficient and standard OLS is appropriate. If you're more interested in minimizing error on blood pressure predictions and aren't concerned with coefficients, then ridge regression is better. Also left out is how we choose the optimal value of lambda by using cross-validation on a selection of lambda values (don't think there's a closed form expression for solving for lambda, correct me if I'm wrong).
Superb. Thanks for such a concise video. It saved a lot of time for me. Also, subject was discussed in a fluent manner and it was clearly understandable.
Fantastic! It's like getting the Cliff's Notes for Machine Learning. These videos are a great supplement/refresher for concepts I need to knock the rust off of. I think he takes about 4 shots of espresso before each recording though :)
These explanations are by far the best ones I have seen so far on youtube ... would really love to watch more videos on the intuitions behind more complicated regression models
You should add in that all the variables (dependent and independent) need to be normalized prior to doing a ridge regression. This is because betas can vary in regular OLS depending on the scale of the predictors and a ridge regression would penalize those predictors that must take on a large beta due to the scale of the predictor itself. Once you normalize the variables, your A^t*A matrix being a correlation matrix of the predictors. The regression is called "ridge" regression because you add (lambda*I + A^t*A ) which is adding the lambda value to the diagonal of the correlation matrix, which is like a ridge. Great video overall though to start understanding this regression.
Hi and thanks fr the video. Can you explain briefly why when the m_i and t_i variables are highly correlated , then the estimators β0 and β1 are going to have very big variance? Thanks a lot in advance!
Sir, a question about 4:54: I understand that in tax/income example the VARIANCE of the beta0-beta1's is high, since there's an additional beta2 effecting things. However, the MEAN in the population should be the same, even with high variance, isn't it so? Thanks in advance!
Excellent approach to discuss Lasso and Ridge regression. It could have been better if you have discussed how Lasso yields sparse solutions! Anyway, nice discussion.
We start out by adding a constraint that beta 1 squared + beta 2 squared must be less than c squared, where c is some number we choose. But then after choosing lamda, we minimize F and c ends up having no effect at all on our choice of the betas. I may be wrong but it doesn't seem like c has any effect on our choice of lambda either. I find it strange that we start out with the criteria that beta 1 squared + beta 2 squared must be less than c squared, but the choice of c is irrelevant. If someone can help me un-boggle my mind that would be great.
Good question - I think it has to do with using the method of Lagrange multipliers to solve the constrained OLS optimization problem. The lambda gets multiplied by the expression in the parentheses at 11:17, which includes the c squared term. So whatever c squared value you choose, it's going to be changed anyways when you multiply by the lambda.
It is unintuitive that we are constraining weights(betas) within value c^2, yet the regularization expression does not include the c but rather sum of squared weights. Certainly I am missing something here. Alternatively, why adding a sum of squared betas(or weights) to the cost function help optimize beta that stays within constraint so that betas don't become large and vary across datasets?
@ritvik when you said that the estimated coefficients has small variance does that implies the tendency of obtaining different estimate values of those coefficients ? I tend to confuse this term 'variance ' with the statistic Variance (spread of the data!).
Variance is the change in prediction accuracy of ML model between training data and test data. Simply what it means is that if a ML model is predicting with an accuracy of "x" on training data and its prediction accuracy on test data is "y" Variance = x - y A smaller variance would thus mean the model is fitting less noise on the training data, reducing overfitting. this definition was taken from: datascience.stackexchange.com/questions/37345/what-is-the-meaning-of-term-variance-in-machine-learning-model Hope this helps.
Can anyone explain the statement "The efficient property of any estimator says that the estimator is the minimum variance unbiased estimator", so what is minimum variance denotes here.
Is the reason to not choose big LAMBDA because we maight get underfitting? If we choose big LAMBDA we get small W and then the output function (hypothesis) won’t reflect our data and we might see underfitting.
Hey Ritvik, I have a question about this one, I don't really know why we are choosing the point that is far from the origin point. So which direction does the gradient descent and why? Please help me out here, thank you so much!
What is the reason behind the use of the ridge regression in the context of use in neural network ensembling such as explained in this article: blog.kaggle.com/2017/10/17/planet-understanding-the-amazon-from-space-1st-place-winners-interview/
How can both beta_1 and beta_2 be bounded by the same C? Are the independent variables normalized? (divided by their variance?) otherwise the scale of beta_1 and beta_2 can be drastically different.
In order to normalize data, we divide it by the standard deviation rather than the variance. And that's just the second step after subtracting the mean.
Well, that is the whole point of regularization, isn't it? You don't want these coefficients to produce a polynomial with the exact fit of your data, i.e. over fitting; you want to have a rough fitting which can only happen when you reject any coefficients, and hence solutions, reside outside the bounded domain (the circle). The answer is you don't care how large are these values, no need to normalize them, you just reject any large that which are not subject to the constrain. If the variation is too high and not recommended to ignore then maybe the Ridge Regression is not the right regularization for your data!
Can anyone help me understanding the effects of multicollinearity? I understand that the estimators will be highly variable, but why would they be very large?
thats actually an interesting question, have you found an explanation to this? I seem to only be able to say that regression depends on variables to be independent on each other, and multicolinearity makes it sensitive to small changes. But why is it that coefficients are larger I cant seem to understand.
This is showing that the quality and value of a video is not depending on how fancy the animations are, but how expert and pedagogue the speaker is. Really brilliant! I assume you spent a lot of time designing that course, so thank you for this!
Wow, thanks!
Totally agree. I learn a lot from his short videos. Precise, concise, enough math, enough ludic examples. True professor mind.
This is the best explanation of Ridge regression that I have ever heard! Fantastic! Hats off!
"Now that we understand the REASON we're doing this, let's get into the math."
The world would be a better place if more abstract math concepts were approached this way, thank you.
good point
Watched these 5 years ago to understand the concept and I passed an exam. Coming back to it now to refresh my memory, still very well explained!
Nice! Happy to help!
This is awesome! Lots of machine learning books or online courses don't bother explaining the reason behind Ridge regression, you helped me a lot by pulling out the algebraic and linear algebra proofs to show the reason WHY IT IS THIS! Thanks!
I was searching for ridge regression on the whole internet and stumbled upon this is a video which is by far the best explanation you can find anywhere thanks.
It's so inspiring to see how you get rid of the c^2! I learned Ridge but didn't know why! Thank you for making this video!
This is, by far, the best explanation of Ridge Regression that I could find on TH-cam. Thanks a lot!
Your data science videos are the best I have seen on TH-cam till now. :)
Waiting to see more
I appreciate it!
This really is gold, amazing!
This really helps me! Definitely the best ridge and lasso regression explanation videos on TH-cam. Thanks for sharing! :D
Excellent video! One more thing to add - if you're primarily interested in causal inference, like estimating the effect of daily exercise on blood pressure while controlling for other variables, then you want an unbiased estimate of the exercise coefficient and standard OLS is appropriate. If you're more interested in minimizing error on blood pressure predictions and aren't concerned with coefficients, then ridge regression is better.
Also left out is how we choose the optimal value of lambda by using cross-validation on a selection of lambda values (don't think there's a closed form expression for solving for lambda, correct me if I'm wrong).
You are the best of all.... you explained all the things,,, so nobody is gonna have problems understanding them.
best explanation of any topic i've ever watched , respect to you sir
This is literally the best video on ridge regression
Amazing video, you really explained why we do things which is what really helps me!
Brilliant! Just found your channel and can't wait to watch them all!!!
I think its explained very fast, but still very clear, for my level of understanding its just perfect !
This is gold. Thank you so much!
You, Ritvik, are simply amazing. Thank you!
I subscribed just after watching this. Great foundation for ML basics
Thanks a lot.. I watched many videos and read blogs before this but none of them clarified at this depth
Thank you soooo much!!! You explain everything so clear!! and there is no way I couldn't understand!
This really helped a lot. A big thanks to you Ritvik!
Stunning! Absolute gold!
seriously!!!
Superb. Thanks for such a concise video. It saved a lot of time for me. Also, subject was discussed in a fluent manner and it was clearly understandable.
Anyone else get anxiety when he wrote with the marker?? Just me?
Felt like he was going to run out of space 😂
Thank you so much thoo, very helpful :)
Fantastic! It's like getting the Cliff's Notes for Machine Learning. These videos are a great supplement/refresher for concepts I need to knock the rust off of. I think he takes about 4 shots of espresso before each recording though :)
The best ridge regression lecture ever.
These explanations are by far the best ones I have seen so far on youtube ... would really love to watch more videos on the intuitions behind more complicated regression models
I'm impressed by your explanation. Great job
Thanks! That means a lot
You should add in that all the variables (dependent and independent) need to be normalized prior to doing a ridge regression. This is because betas can vary in regular OLS depending on the scale of the predictors and a ridge regression would penalize those predictors that must take on a large beta due to the scale of the predictor itself. Once you normalize the variables, your A^t*A matrix being a correlation matrix of the predictors. The regression is called "ridge" regression because you add (lambda*I + A^t*A ) which is adding the lambda value to the diagonal of the correlation matrix, which is like a ridge. Great video overall though to start understanding this regression.
So so so very helpful! Thanks so much for this genuinely insightful explanation.
Your explanation is extremely good!
Shouldn't the radius of the Circle be c instead of c^2 (at time around 7:00)?
It's just awesome. Thanks for this amazing explanation. Settled in mind forever.
The explanation is so clear!! Thank you so much!!
Excellent explanation! Could you please do a similar video for Elastic-net?
in your drawing at 9:00, if the level curves is reverted back to 3D graph, is the axis that going up the loss function? just want to clarify. thanks!
Very good explanation in an easy way!
Hi and thanks fr the video. Can you explain briefly why when the m_i and t_i variables are highly correlated , then the estimators β0 and β1 are going to have very big variance? Thanks a lot in advance!
Hi same question here😶🌫
Awesome, Thanks a Million for great video! Searching you have done video on LASSO regression :-)
best explanation on ridge reg. so far
THIS IS ONE HELL OF A VIDEO !!!!
I was looking for the math behind the algorithm. Thank you for explaining it.
No problem!
Sir, a question about 4:54: I understand that in tax/income example the VARIANCE of the beta0-beta1's is high, since there's an additional beta2 effecting things. However, the MEAN in the population should be the same, even with high variance, isn't it so? Thanks in advance!
Thank you. I make the comment because I know I will never need to watch it again! Clearly explained..
Glad it was helpful!
Brilliant simplification of this topic. No need for fancy presentation to explain the essence of an idea!!
I don't have money to pay him so leaving a comment instead for the algo. He is the best.
Stunning!! Need more access to your coursework
I think it's the best video ever made
you are the man, keep doing what you're doing
Finally, someone who talks quickly.
Brilliant! Could you make more videos about Cross validation, RIC, BIC, and model selection.
Excellent approach to discuss Lasso and Ridge regression. It could have been better if you have discussed how Lasso yields sparse solutions! Anyway, nice discussion.
great video, brief and clear.
excellent video! Keep up the great work!
great video, the explanation is really clear!
We start out by adding a constraint that beta 1 squared + beta 2 squared must be less than c squared, where c is some number we choose. But then after choosing lamda, we minimize F and c ends up having no effect at all on our choice of the betas. I may be wrong but it doesn't seem like c has any effect on our choice of lambda either. I find it strange that we start out with the criteria that beta 1 squared + beta 2 squared must be less than c squared, but the choice of c is irrelevant. If someone can help me un-boggle my mind that would be great.
Good question - I think it has to do with using the method of Lagrange multipliers to solve the constrained OLS optimization problem. The lambda gets multiplied by the expression in the parentheses at 11:17, which includes the c squared term. So whatever c squared value you choose, it's going to be changed anyways when you multiply by the lambda.
SUPER !!! You have to become a professor and replace all those other ones !!
Excellent explanation, thanks!
simple and effective video, thank you!
Thank You, Great Video! Just a possbile correction, at 6:35 shouldn't the radius be c instead of c^2?
Dorukhan Sergin probably late, but no equation of circle is x^2 + y^2 = r^2
Thanks! why lamba cannot be negative? What if to improve variance it is need to increase the slope and not decrease?
Dude ! Hats off 🙏🏻
It is unintuitive that we are constraining weights(betas) within value c^2, yet the regularization expression does not include the c but rather sum of squared weights. Certainly I am missing something here. Alternatively, why adding a sum of squared betas(or weights) to the cost function help optimize beta that stays within constraint so that betas don't become large and vary across datasets?
Amazingly helpful. Thank you.
I would trade diamonds for this explanation (well, allegorically! :) ) Thank you!!
Excellent explanation .
what the "level curve" means?
What is the intuition behind putting the constraint on the size of the Beta coefficient rather than the standard errors of the Beta coefficient?
best explanation ever!
@ritvik when you said that the estimated coefficients has small variance does that implies the tendency of obtaining different estimate values of those coefficients ? I tend to confuse this term 'variance ' with the statistic Variance (spread of the data!).
Variance is the change in prediction accuracy of ML model between training data and test data.
Simply what it means is that if a ML model is predicting with an accuracy of "x" on training data and its prediction accuracy on test data is "y"
Variance = x - y
A smaller variance would thus mean the model is fitting less noise on the training data, reducing overfitting.
this definition was taken from: datascience.stackexchange.com/questions/37345/what-is-the-meaning-of-term-variance-in-machine-learning-model
Hope this helps.
@@benxneo thanks mate!
It is a brilliant video. Great
Can anyone explain the statement "The efficient property of any estimator says that the estimator is the minimum variance unbiased estimator", so what is minimum variance denotes here.
Beautiful explanation
Thank you! Your explaining is really good, Sir. Do you have time to make a video explaining the adaptive lasso too?
Is the reason to not choose big LAMBDA because we maight get underfitting? If we choose big LAMBDA we get small W and then the output function (hypothesis) won’t reflect our data and we might see underfitting.
Great videos thanks for making it
I love this video, really informative! Thanks a lot
Hey Ritvik, I have a question about this one, I don't really know why we are choosing the point that is far from the origin point. So which direction does the gradient descent and why? Please help me out here, thank you so much!
great video - thanks
This is gold indeed!
You are awesome!
great video! thank you very much.
Great video. A (very minor) question: isn't it c instead of c^2 when you draw the radius vector of the circle for \beta restriction?
think of it as an equation of a circle with center (0,0)
Awesome video! Very intuitive and easy to understand. Are you going to make a video using the probit link?
excellent video! thank you!
excellent video, thanks.
awesome video, thank you very much!
What is the reason behind the use of the ridge regression in the context of use in neural network ensembling such as explained in this article:
blog.kaggle.com/2017/10/17/planet-understanding-the-amazon-from-space-1st-place-winners-interview/
Can someone explain what the level curves mean?
Google contour plots, not something that can be easily explained on a video. Usually taught in first few lessons of Calculus III.
and , is c a value that minimizes VIF value?
thanks for the nice explanation
hey, great video and excellent job
How can both beta_1 and beta_2 be bounded by the same C? Are the independent variables normalized? (divided by their variance?) otherwise the scale of beta_1 and beta_2 can be drastically different.
In order to normalize data, we divide it by the standard deviation rather than the variance. And that's just the second step after subtracting the mean.
also you can do apply MinMax Scaler... in sklearn for Ridge and Lasso there is "normalize" parameter. normalize : boolean, optional, default False
Well, that is the whole point of regularization, isn't it? You don't want these coefficients to produce a polynomial with the exact fit of your data, i.e. over fitting; you want to have a rough fitting which can only happen when you reject any coefficients, and hence solutions, reside outside the bounded domain (the circle). The answer is you don't care how large are these values, no need to normalize them, you just reject any large that which are not subject to the constrain. If the variation is too high and not recommended to ignore then maybe the Ridge Regression is not the right regularization for your data!
Can anyone help me understanding the effects of multicollinearity? I understand that the estimators will be highly variable, but why would they be very large?
thats actually an interesting question, have you found an explanation to this? I seem to only be able to say that regression depends on variables to be independent on each other, and multicolinearity makes it sensitive to small changes. But why is it that coefficients are larger I cant seem to understand.
Very clear. Thank you!
bless this is amazing
6:30 It should be c, not c^2 on the diagram
Thank you, this was tripping me up.