Man, its such a privilege being able to watch stuff like this.
@Biesterable5 жыл бұрын
So true
@TrentTube4 жыл бұрын
I feel the exact same way. I am constantly humbled and thrilled this is available.
@filippovannella49575 жыл бұрын
This man is one of the best professor I have ever seen. Thanks a lot for this lecture series.
@ebiiseo4 жыл бұрын
Your ability to uncover insights behind all those mathematical formulas is superb. I really like the way you teach. Thank you for uploading this
@jorgeestebanmendozaortiz8733 жыл бұрын
Due to the Covid crisis the professors at my University went on a strike for most of the semester, so my ML class got ruined. Fortunately I found your lectures, and I've been following through the last months. I have to say this is the most thorough introductory course to ML that I've found out there. Thank you very much, prof. Killian, for making your lectures available for everyone. You're working towards a freer and better world by doing so.
@tarunluthrabk3 жыл бұрын
I searched extensively for good content on Machine learning, and by God's grace I found one! Thank you Prof Weinberger.
@jachawkvr4 жыл бұрын
I was familiar with these concepts before watching this lecture, but now I feel like I actually understand what bias and variance mean. Thank you so much for explaining these so well!
@yuniyunhaf57675 жыл бұрын
i cant believe i have reached to this point, and he shaped the way i think about ML, best professor
@juliocardenas44853 жыл бұрын
I’m using what I’ve learned here to try improving people’s lives. I’m a data scientist in healthcare and a former radiology researcher. Thank you for sharing this freely.
@muratcan__225 жыл бұрын
this video is gold
@deltasun4 жыл бұрын
that's the clearest exposition of bias-variance decomposition I've ever seen (and i've seen quite a few). by far
@kevinshen32212 жыл бұрын
this is absolutely gold. was so confused by reading An Introduction to Statistical Learning because they give no explanation of how they get bias variance tradeoff, and i found this!
@xwcao19913 жыл бұрын
Thank you prof. Weinberger for making educational fairness to the people from the thrid world countries like me. who can not afford to study in one of the world's class universities like Cornell. Wish you healthy and happy in your entrie life.
@MohamedTarek-vt4lb8 ай бұрын
This is Amazing! bless you professor Kilian if you read this
@psfonseka5 жыл бұрын
This was super helpful for my own classwork. Thank you so much for posting your lectures publicly!
@vatsan164 жыл бұрын
Me: Machine learning is a black box, the math is too abstract, and nothing really makes sense Professor Weinberger: Hold my beer
@jenishah98252 жыл бұрын
Such videos don't generally come up in YT suggestions. But if you have found it, it is a gold mine!
@rajeshs28404 жыл бұрын
Oh Man, Hats off to you efforts.. Its amazing lecture..
@vishnuvardhan66255 ай бұрын
Best vedio on Bias-Variance Decomposition ❤
@mateuszjaworski29748 ай бұрын
It's like a good action movie, you can't wait enought about what will be next.
@crystinaxinyuzhang36214 жыл бұрын
It's such an amazing lecture! I've never thought each trained trained ml model itself as a random variable before and this is really eye opening
@haodongzheng70452 жыл бұрын
Thank you, professor. I feel like that I’ve grown up a little bit after watching your video ;)
@sans81194 жыл бұрын
An amazing lecture !! makes things very clear .
@sheikhshafayat69843 жыл бұрын
I don’t usually comment anywhere. But I can’t help say a thanks to you. Such a great teaching skill!
@taketaxisky4 жыл бұрын
The way the error is decomposed reminds me of the decomposition of sum of squares in ANOVA into within group SS and between group SS, in a similar calculation
@vishchugh4 жыл бұрын
BEST LECTURE ON BIAS VARIANCE TR !!!!!!!!!!!!!!!!
@angelocortez51852 жыл бұрын
These videos popped up on my feed. Didn't realize you wrote the MLKR paper as well. Seeing your videos make me wish I took a formal class with you. Thank you for this content Kilian!
@TheAIJokes3 жыл бұрын
you are one of my favourite teacher sir....love you from india....❤️
@NO_REPLY_ALARM_TOWARD_ME Жыл бұрын
I think that the lecturer always give the students several minutes to make clarified themselves even it maybe seems to be trivial in proving step. It maybe seem difficult, but concise to follow. Thanks.
@noblessetech4 жыл бұрын
Awesome video playlist love it.
@abhyudayasrinet175 жыл бұрын
A really great explanation
@florianwicher3 жыл бұрын
It was a little bit slow, but I got it now. Thanks a lot!
@ashraf736 Жыл бұрын
What a wonderful lecture.
@hanseyye14683 жыл бұрын
Thanks Professor Weinberger.I have one question on 23:28, why we use here the joint distribution p(x,y) but not a conditional p(yIx) or p(y)*p(x)
@kilianweinberger6983 жыл бұрын
Because you are drawing x and y randomly, and your data set and algorithm depends on both. You could factor this into first drawing x, then y i.e. P(y|x)P(x), but it really wouldn't change much in the analysis. Hope this helps.
@hanseyye14683 жыл бұрын
@@kilianweinberger698 thank you so much
@jordankuzmanovik52974 жыл бұрын
Wonderful!!...Bravo
@janismednieks12773 жыл бұрын
"My son is doing that now, he's in second grade." If you're the one teaching him, I believe you. Thanks.
@xmtiaz2 жыл бұрын
This was beautiful.
@StevenSarasin9 ай бұрын
That means that the noise also depends on the feature set. So that the noise is not necessarily irreducible, if you can find new features to include. In the housing price example you would appear to have a lot of noise if you left out a location variable in the feature x! Interesting. So we have reduced the generalization error to the dependency on D, the variance, will more data improve the situation? the dependency on the feature set, does there exist a feature set that limits the variance on y itself averaged given x? and there is the bias dependency, are we in principle flexible enough to match the true data pattern (linear vs non-linear.)
@immabreakaleg4 жыл бұрын
17:48 what a boss question wow
@Saganist4205 жыл бұрын
My real life dart playing skills have high bias, high variance.
@VijayBhaskarSingh2 жыл бұрын
{x1, x2, .. xi} are sample vectors from (X variables)? Or they are function of one variable?
@meenakshisundaram83103 жыл бұрын
Thank you very much
@gauravsinghtanwar44154 жыл бұрын
What is the need to take probability term in the expected test error expression ?
@utkarshtrehan91283 жыл бұрын
Enlightenment
@danielsiemmeister52862 жыл бұрын
First of all thank you of this very intuitive explanation, Mr. Weinberger! I have some small questions or remarks which aren't 100 % clear to me: - you said, that y (given x) is random. So we want to pick one statistic depending on our goals. In this case you choose the Expectation(y|x). (One could for example choose the median, coudn't we?) However some minutes later you choose the squared loss function as a "nice" choice for regression. Aren't this two sides of the same coin? If I am choosing the squared loss function, then I am picking the E[y|x]? (When I am choosing the absolute value loss function, then I am choosing the median). So this is my first question, are my thoughts right? - How would the proof look like if I am not in the "squared loss / expectation" setting? What would the proof look like for an generic loss function or statistic of y|x? This is my second question. - How would the proof look like if we are going in the regression setting? I think that is pretty much the same question as question 2. Am I right, when I am saying, that if the distribution of y|x is discrete, than I am in a classification setting and if it is continous, than I am in a regression setting? Furthermore, if I am picking the statistic of y|x (or a loss function) in a generic way, then I have a proof for classification and regression problems? I would be very thankful if anyone could answer or comment on my questions! Yours Daniel
@kilianweinberger6982 жыл бұрын
Yes, you are right. The math becomes a lot trickier if you don't use the squared loss, but ultimately the principle is the same for pretty much any less function.
@ayushmalik70932 жыл бұрын
Hi Prof High Variance implies overfitting but overfitting has 2 parts, high test error and low training error. how to imply low training error from high variance? High variance in the hd(x) could also be result of gibberish learning by our algo which could leads to high test and training error. IMO low bias and high variance should mean overfitting as in that case model prediction for different datasets will spread around the centre of your dart board.
@sandeshhegde91435 жыл бұрын
Where is lecture 18? (I don't see it in the playlist)
@Saganist4205 жыл бұрын
lecture 18 was an exam, so it was not recorded.
@TrentTube4 жыл бұрын
I eventually concluded it was the exam I skipped :D
@amit_muses4 жыл бұрын
I have a command on Bayesian probability theorem, total probability theorem, but couldn't understand the symbols the prof used. I could understand that the prof used some concepts of Expectation theory but couldn't understand well. Can someone suggest some material for this part that I can do in a very short period so that I can understand this lecture well
@adiratna962 жыл бұрын
I didn't understand why D and (x,y ) are independent. Anyone can explain why? please. TIA.
@adiratna962 жыл бұрын
Damn, never mind I got it.
@lorenzoappino91583 жыл бұрын
Killian is my hero
@siddhanttandon62462 жыл бұрын
Hey Prof i have a question. In this derivation we kinda bounded the risk for a new sample i.e. out of sample risk which is composed of 3 parts. Is their some theory which does the same breakdown of risk on our training set i.e. samples the model has already seen ? I am particularly interested to know if my training loss can ever go to zero.
@kilianweinberger6982 жыл бұрын
That depends on your hypothesis class (i.e. what algorithm you are using). Maybe take a look at the lectures on Boosting. AdaBoost is an ensemble algorithm that (given some assumptions) guarantees that the training error will go to zero (if you average several classifiers together).
@ammarkhan26114 жыл бұрын
Hi Professor, Is there a way to get an access to the assignments ?
@pendekantimaheshbabu97994 жыл бұрын
Excellent Can we apply bv trade off among different models?ie for e.g. between Linear Regression and polynomial regression comparison?Whether Bold H consists of set of Hypotheses that contain only linear regressors?
@kilianweinberger6984 жыл бұрын
Ultimately the BV trade-off exists for all models. However, as far as I know the derivation of this decomposition only falls into place so nicely in a few steps for linear regression.
@roniswar3 жыл бұрын
Dear Prof', Thank you again for posting this, very useful and interesting!! One question: in a regression setup, why do you call h (the hypothesis function) as "expected classifier"? Is this the common definition, when thinking about regression problem? Thanks!
@kilianweinberger6983 жыл бұрын
No, it is only in the setting where you consider the training set as a random variable. Under this view, the classifier also becomes a random variable (as it is a function of the training set), and you can in theory compute its expectation. Hope this helps.
@roniswar3 жыл бұрын
@@kilianweinberger698 Thank you! One other thing that I didn't see that anyone asked. What happens to the The bias-variance tradeoff, that you fully showed for MSE, when the loss function is not an MSE? Is the decomposition still contains exactly those 3 quantities of bias-variance-noise? How do we measure the tradeoff in these case? We do not longer have this convex parabola shape I assume (If you have a good source explaining this issue please refer me to it).
@macc73743 жыл бұрын
Hi Professor! Thank you for uploading this video. When we start the derivation by representing expected test error in terms of hD(X) and y, how can we explain the presence of noise? Our assumption is that y is the correct label. So while there is certainly noise in real world examples, given the starting point of the derivation here, should noise be expected to show up?
@kilianweinberger6983 жыл бұрын
Keep in mind noise can either be a bad measurement, but it could also be part of the label that you just cannot explain by your representation of x. Imagine I am predicting house prices (y) based on features about a house (x). My features are e.g. number of bedrooms, square footage, age, ... But now the price of a house decreases because a really loud and rambunctious fraternity moves in next door - something that is not captured in my x at all. For this house the price y is now abnormally low. The price is correct, but given your limited features the only way you can explain it is as noise.
@macc73743 жыл бұрын
@@kilianweinberger698 thank you
@gaconc13 жыл бұрын
This is a form of the Pythagorean theorem
@kilianweinberger6983 жыл бұрын
Interesting observation!
@logicboard77462 жыл бұрын
Point @22:00
@logicboard77462 жыл бұрын
Then @41:00
@taketaxisky4 жыл бұрын
How does overfitting affect the decomposed error terms? Maybe it is not relevant here.
@taketaxisky4 жыл бұрын
Just realize a graph in the lecture notes explains this!
@kc12993 жыл бұрын
disappears into some good feeling hahhaa
@bharatbajoria3 жыл бұрын
Why is there no D at 37:00 in b^2?
@kilianweinberger6983 жыл бұрын
both terms y-bar and y are independent of the training data set D.
@deepfakevasmoy34774 жыл бұрын
24:56 please someone ask some question, I am not ready for war :)
@hohinng8644 Жыл бұрын
Everything is excellent except the poor handwritting