I dont think mathematical explanation given in this video exist in youtube. I have found this in the book "Mathematics for Machine Learning by Marc Peter Deisenroth". This is Simply brilliant. Although, matrix differentiation part is absent, but still this is extra ordinary stuff.
Sir I Can tell You No One Literally No One Video Can Compare through your teaching, I have seen videos of Coding Ninjas and Other Paid Lectures but nobody has got into this dept , I can literally feel Machine Learning in Front of My Imagination. Thank You So Much Sir 🙏
sir bohot sahi pdhate ho aap to....pta nhi kisi ne pehle suggest kyu nhi kiya mujhe aapka channel....not only practical coding but also the theory part, you explain in detail
Big fan of your teaching watching this video for 2nd time to revise and brush up all my concepts and make sure I remember them and be able to derive the equation if asked me anytime, any day 🙂
Doubt Sir ji 🙏 36:00 When you differentiate the matrix considering Y = A'XA Your answer is 2XA^T ..while the answer should be dY/dA = 2XA not the transpose .. correct me if I am wrong plzz
*->Transpose y*(XB)=(XB)*Y can be prove after taking XB=Y(hat) and put them with their respective matrices. y=[y1 y2 yn] y(hat)=[y(h)1 y(h)2...y(n)] putting into equation will prove both are same
No Doubt sir your teaching is so fantastic I am following your videos Sir I have one doubt in the step where you do X^TXB^T=y^TX B^T=Y^TX(X^TX)^-1 but it shouldn't be B^T=(X^TX)^-1Y^TX basically inverse term must be pre multiplied because we pre multiply by inverse term to cancel it out on left hand side and matrix multiplication is not commutative so we can't write it on other side Please clear my doubt
37:23 sir i have a doubt if i multiply LHS by (X`T X)'-1 i will be left with B'T on LHS so therefore i need to multiply RHS also by same term right. But if i do so i'll get some other answer. why is this sir.
Hi Nitish sir, while calculating the error function we used differenctiation to get the expression but in the very beginnning you said we don't use calculus for ols and for gradient descent we do but we used that in both so how it is closed form or non closed form? whats the concept I got it , but closed and non closed form how they're diff as we're doing differentiation in both of them ? Thanks for these videos.
he used calculus to show how ols equation is formed from scratch. In ols machine use final equation to calculate best fit line but in gradient descent it use calculus to reach minima point.
13:09 matrix multiplication is wrong When X is multiplied by B it should give a matrix of single column While the matrix described earlier is of m coloums
@CampusX Can someone explain what would happen if the Inverse doesn't exist for that particular matrix in the last step(X^T.X)^-1 i.e. if the determinant is 0?
The reason is simple. See, X is the matrix consisting of features. Now, there are 2 possibilities for non-existance of the inverse of (X^T.X)^-1; first one is X is a null matrix and hence X^T is also a null matrix; second possibility is X^T.X is a null matrix (but none of them is individually null). You can skip the first possibility because if feature matrix is null nobody cares about the problem. Coming to the 2nd possibility, X is a (nx1) and X^T is a (1xn) matrix; X^T.X will be a (1x1) matrix. Now even if some elements of X^T are negative , it will be multiplied with the same element of X ( Notice : ith element of the 1st row of X^T == ith element of the 1st column of X ) . Hence while multiplicating and adding the elements while performing X^T.X you will never come across any negative element. So, addition of all positive quantity will give you a positive (1x1) matrix. Hence, inverse of X^T.X will always exist.
sir , at 36:26 i think you used d/dA( A^TxA) = 2xA^T but its 2xA.... so i'm little confused about the last final result 🫤..only this thing else everything , you are great sir ...love your videos .
The video is awesome. I have a doubt though. At 37:35 you premultiply the inverse on the LHS but post multiply on RHS. Isn't that wrong? Correct me if I am missing something
I dont think mathematical explanation given in this video exist in youtube. I have found this in the book "Mathematics for Machine Learning by Marc Peter Deisenroth". This is Simply brilliant. Although, matrix differentiation part is absent, but still this is extra ordinary stuff.
yes , Well said .. brilliantly explained :-)😍😍😍😇😇
@@SidIndian082 yup, the explanation was damn good...
Sir I Can tell You No One Literally No One Video Can Compare through your teaching, I have seen videos of Coding Ninjas and Other Paid Lectures but nobody has got into this dept , I can literally feel Machine Learning in Front of My Imagination. Thank You So Much Sir 🙏
40:00 It is worth mentioning that for any matrix ( X ), the product ( X^T X ) is always symmetric.
nitish sir and his love for cgpa and lpa dataset is a never ending lovestory😂 anyways....by far the best explanation.... Thankyou sir.
sir bohot sahi pdhate ho aap to....pta nhi kisi ne pehle suggest kyu nhi kiya mujhe aapka channel....not only practical coding but also the theory part, you explain in detail
This is the best video. where I have again made myself sure that I want to become a successful data scientist.
Hi Sir..U r truly gem person sharing such a great knowledge free..is blessing for new generation..god bless u sir..Aap hamare Guru ho Aaj Se..
literally, it was the greatest explanation that I have ever seen on TH-cam. Hat's off Sir
thanks Nitesh for producing such high quality content.
Completed on 12:07PM 9th September 2024
Made complex things so easy . i.e, CampusX
Such wonderful explanation sir, really thanks a lot♥️♥️♥️you were able to explain something which 100s of videos couldn't explain to me.
I jumped when I understood eT*e concept. Thank you so much!!!
Most underrated channel on utube 🥲
Big fan of your teaching watching this video for 2nd time to revise and brush up all my concepts and make sure I remember them and be able to derive the equation if asked me anytime, any day 🙂
Eagerly waiting for next video😁😉. Thank you so much sir for this🙏❤️
Have u achieved your dream now ? Please say yes
0:30-->2:45 intuition behind MLR
43:20-->47:45 Why gradient descent is more effective as compared to OLS?
Thank you very much for the explanation sir, I searched the whole youtube to get this mathematical explanation!
Itna saare phle pdha kese bhaiya apne.....
Suprrrrr se uprrrrrr vla h, wowooooooooo...
Man top class stuff, been trying to find mathematical derivation from many days in TH-cam.
Superb content ,easily my semester
saviour at IIT Kanpur...Thanks Sir
Boss tusi great ho ❤️ struggling straight from 1 months 🙃
step by step series in very detail , superb .
Matchless way of teaching
34:18 shouldn't its differentiation be equal to (X^T)y which is transpose of X times y instead of transpose of y times X which is (y^T)X.
you are an amazing teacher. never saw with such good explanations on youtube. Love from pakistan
Doubt Sir ji 🙏
36:00
When you differentiate the matrix considering Y = A'XA
Your answer is 2XA^T ..while the answer should be dY/dA = 2XA not the transpose .. correct me if I am wrong plzz
Yes, I have the same query as well. In the gatsby document also 2AX is mentioned.
*->Transpose
y*(XB)=(XB)*Y can be prove after taking XB=Y(hat) and put them with their respective matrices.
y=[y1 y2 yn]
y(hat)=[y(h)1 y(h)2...y(n)]
putting into equation will prove both are same
My master's prof. can't explain things better than you ! Thank you for making such awesome videos !
Simple and elegant explanation.
GOD LEVEL TEACHING SKILL 💡💡
This ML series is making me interested in maths of Machine Learning algorithms.
No Doubt sir your teaching is so fantastic I am following your videos
Sir I have one doubt in the step where you do
X^TXB^T=y^TX
B^T=Y^TX(X^TX)^-1
but it shouldn't be B^T=(X^TX)^-1Y^TX basically inverse term must be pre multiplied
because we pre multiply by inverse term to cancel it out on left hand side and matrix multiplication is not commutative so we can't write it on other side
Please clear my doubt
that what I thought, it is wrong in the video
Sir you are the best teacher
37:23 sir i have a doubt if i multiply LHS by (X`T X)'-1 i will be left with B'T on LHS so therefore i need to multiply RHS also by same term right. But if i do so i'll get some other answer. why is this sir.
You are Genius!
love you sir, with all respect.
Beautiful, luckily I know it before but awesome teaching skills
Thank You Sir.
Thank you so much sir 🙏🙏🙏
Mathematical Explaination☠☠ Code😊😊
no one made the maths this interesting until today
Thank you so much!
35:40 where is video of matrix differentiation , there is no link is description
36:00 bhiya kindly upload video on matrix differentiation.
Thank you for making such fantastic videos!
You are a Gem, Sir. Keep it up. Thank you!
Bhai did you make video about matrix differention you mention in the vidoe ? If yes kindly please provide the link
best explain
Hello Sir, XGBoost is not included in playlist, could you please make a video on XGBoost ?
Wonderful sir
Bahat badi baat bool di aj ap ne
Hi Nitish sir, while calculating the error function we used differenctiation to get the expression but in the very beginnning you said we don't use calculus for ols and for gradient descent we do but we used that in both so how it is closed form or non closed form? whats the concept I got it , but closed and non closed form how they're diff as we're doing differentiation in both of them ?
Thanks for these videos.
he used calculus to show how ols equation is formed from scratch. In ols machine use final equation to calculate best fit line but in gradient descent it use calculus to reach minima point.
@@spynom3070 thanks for this.
Really amazing video sir.
SIr... shouldnot after differentiation and reduction we will be left with yT=XTBT which again transposed gives y=XB and there fore B=X^-1y?
Please make detail video on matrix diff.
13:09 matrix multiplication is wrong
When X is multiplied by B it should give a matrix of single column
While the matrix described earlier is of m coloums
I guess the Y hat(matrix before decomposing) should be equal sum of each columns as ine column so Y hat will be of n*1 order
Then it would be correct
Yeah he just forgot to put addition sign in between terms
@@titan_471 Yes , you're right , He should have put + sign between the terms
sir apny matrix differentiation ka video nahi dala hai
Matrix differentiation video please upload sir @campusx
Thank you so much.
Thank you for this sir!
bosss that was awesome
Math guru as well as machine learning
1 no. sir
done ✅
Loss function 1/2m se start hota hai sir ?
@CampusX Can someone explain what would happen if the Inverse doesn't exist for that particular matrix in the last step(X^T.X)^-1 i.e. if the determinant is 0?
Very nice question but iska answer mujhe bhi nahi patha
The reason is simple. See, X is the matrix consisting of features. Now, there are 2 possibilities for non-existance of the inverse of (X^T.X)^-1; first one is X is a null matrix and hence X^T is also a null matrix; second possibility is X^T.X is a null matrix (but none of them is individually null). You can skip the first possibility because if feature matrix is null nobody cares about the problem. Coming to the 2nd possibility, X is a (nx1) and X^T is a (1xn) matrix; X^T.X will be a (1x1) matrix. Now even if some elements of X^T are negative , it will be multiplied with the same element of X ( Notice : ith element of the 1st row of X^T == ith element of the 1st column of X ) . Hence while multiplicating and adding the elements while performing X^T.X you will never come across any negative element. So, addition of all positive quantity will give you a positive (1x1) matrix. Hence, inverse of X^T.X will always exist.
campusX > MIT
sir , at 36:26 i think you used d/dA( A^TxA) = 2xA^T but its 2xA.... so i'm little confused about the last final result 🫤..only this thing else everything , you are great sir ...love your videos .
Actually na, the differentiation is (X+X^T).A^T. If X=X^T then it becomes 2xA^T.
Sir actually I had a doubt, d/da of At*x*A is 2XA but you have written 2XA transpose, can you explain it?
Thank you sir 👍
Awsome
@campusx sir Y(hat)=B0+B.X1+B2.X2......Bn.Xn tha to matrix me different element kaise ho gya????
The video is awesome. I have a doubt though. At 37:35 you premultiply the inverse on the LHS but post multiply on RHS. Isn't that wrong? Correct me if I am missing something
Yes correct ..The final value of beta should be: (( X transpose)Y)((X transpose)X)^-1
@@readbhagwatgeeta3810 thnxx
done
(AT)-1 = (A-1)T
using this formula you can prove the last part
[(XTX)-1]T = (XTX)-1
matrix differentiation ki video kab aaegi
❤
ily!
(best best best best ......best)^best
Hell sir Do you have notes ??
🎉🎉🎉❤
Day4
Date:12/1/24
4:03 Universal problem 🤣