I'm so glad that I found this lecture! Multivariate normal distribution was making no sense to me when I was starting at the page in my textbook. Your examples are superb and they build intuition very well. Love this!
I am eternally grateful for you.a teacher like you is what we students need .i didn't feel hint of doubt in this whole video of 53 mins.The only thing I could be is grateful for you .this world needs more teacher like you.i respect your profession and YOU sir. Thankyou so much
Thanks very for this video...it really helped me. Dr. Please regarding the independence assumption, do we always assume the given variables are independent. Hoping to hear from you in your soonest possible time.
Amazing explanation. Had to go though many videos in order to get an explanation that makes sense. I just have a small question. in the minute 16:57 he talks about matrix multiplication. He mentions (X^T) X is the square of a matrix. Can someone elaborate on this matrix identity. I have tried google but havent seen a straight answer. Thanks in advance!
First search (1)how matrix multiplication works, then search (2)what is a transpose. Then you will realize, if X is a vector of 3 elements [123] then (X^T)X is a square of X i.e. [1 4 9]
@@ishansgyan8665 Your answer is wrong on multiple counts. As per your example, if X = [1 2 3], the result of (X^T)X would be a 3x3 matrix, not the elementwise squares. Infact, @clusterknight is right, there is no such identity that (X^T)X is the square of the matrix X. If you calculate what you have said, you will get a square matrix whose diagonal elements will be the elementwise squares. Also, what is present in the exponent is not a simple (X-Mu)^2 , the result that he has shown is not possible without involving the SIGMA matrix.
@@chandramoulisanthanam6964 in my example I didn't emphasize on matrix structure. For diagonal matrix (x'x) will be a matrix with squared of elements of X, this will be obtained by sigma matrix in the video, which will diagonalize it
Doesn't matter sigma 12 will always be equal to sigma 21 👏😂😂 2 year late..now this comment won't be useful at all .but it will recall you that moment when you spend your time over this video Have fun😂😂
Hanzala Jamash, because, off diagonal elements in the matrix show covariance I.e how much they're dependent on each other... Since here he took example of independent variables covariance is zero hence sigma 12 is zero
Sigma squared is nothing but Cov(X,X) in co variance matrix which equals to Var(X) . so for variable X1 its sigma1 squared and for variable X2 its sigma 2 squared
The best tutorial on the subject I found amongst many others. Thank you very much.
My native English speaking Stats prof. could only dream of being this clear... Thank you very much!
How do you know that he is not a native English speaker?
+bonn germany obviously the accent :). Still very good to understand.
He is an Indian.
my prof is busy hovering his mouse pointer over slides rather than putting some effort into writing a single word.
I'm so glad that I found this lecture! Multivariate normal distribution was making no sense to me when I was starting at the page in my textbook. Your examples are superb and they build intuition very well. Love this!
How come most professors don't lecture with such clarity like Dr Maiti?
You're awesome sir!
I am eternally grateful for you.a teacher like you is what we students need .i didn't feel hint of doubt in this whole video of 53 mins.The only thing I could be is grateful for you .this world needs more teacher like you.i respect your profession and YOU sir.
Thankyou so much
What a clear and an excellent teaching method!
Now IK, everything, Hats off to the Prof. Love his teaching style.
Probably the best explanation of MVND that I have seen so far.
This is brilliant teaching, really clear and the right pace to grasp the material!
You sir are the best tutor in youtube for this. I salute you.
nptelhrd is one of the best channels on UA-cam!
Thank you!
Clearly explained all the concepts, thanks for making the video on such complex topic and making it easier.
Very helpful.
This is GOLD. Thank you so much! Proud of my alma mater.
Thank you very much Dr for the much needed clarity.
Amazing lecture with extraordinary clarity.
Share brilliance Dr. Love the way you explain different terms in detail. Please keep on adding more of your videos.
Sir your explaining style is very good plz also upload your lectur on wishart distribution as well
What a clear explaination. Thanks! I'm very appreciate this, hats off!
Now I know why are IIT students are so intelligent. Wished the same professor in our class...
Wonderful...sir. The best video for understanding this concept.
Splendid teaching professor! Thank you so much.
Thank you sir. comprehensive, precise and clear.
The best lecture I found useful!
🙂🙂 ... Proud Indian math lover
You need patience to watch it .. But it is worth it.
Simply fantastic. Thank you very much
Vary nice lecture...
Thank u vary much sir...
Very nicely explained. Respect !
This lecture is very good. Very well explained.
Superb sir..showing the practical aspect of mathematics...Nice
Cool!
This is really great. Thanks, sir!
Its a very usefull and good lecture, It helps me alot
Thanks very for this video...it really helped me.
Dr.
Please regarding the independence assumption, do we always assume the given variables are independent.
Hoping to hear from you in your soonest possible time.
Very nice explanation! Thank you sir!
God bless Prof. Maiti👏👏
thank you very much, great explanation!
Awesome Explanation.
Thank you so much! Clear and easy to understand!
amazing! thank you so much!
Great lecture sir!
The best Dr ever
Amazing explanation. Had to go though many videos in order to get an explanation that makes sense.
I just have a small question. in the minute 16:57 he talks about matrix multiplication. He mentions (X^T) X is the square of a matrix. Can someone elaborate on this matrix identity. I have tried google but havent seen a straight answer. Thanks in advance!
First search (1)how matrix multiplication works, then search (2)what is a transpose. Then you will realize, if X is a vector of 3 elements [123] then (X^T)X
is a square of X i.e. [1 4 9]
thanks bro @@ishansgyan8665
@@ishansgyan8665
Your answer is wrong on multiple counts.
As per your example, if X = [1 2 3], the result of (X^T)X would be a 3x3 matrix, not the elementwise squares. Infact, @clusterknight is right, there is no such identity that (X^T)X is the square of the matrix X. If you calculate what you have said, you will get a square matrix whose diagonal elements will be the elementwise squares. Also, what is present in the exponent is not a simple (X-Mu)^2 , the result that he has shown is not possible without involving the SIGMA matrix.
@@chandramoulisanthanam6964 in my example I didn't emphasize on matrix structure.
For diagonal matrix (x'x) will be a matrix with squared of elements of X, this will be obtained by sigma matrix in the video, which will diagonalize it
@@ishansgyan8665 is (x-u) is a diagonal matrix?
5:18 shouldn't the elements of your covariance matrix be squared? Otherwise as it is would be a standard deviation matrix.
thank you very much
Superb ..thank you so much 👍
You sketch pen gives me anxiety but still I manged to watch the whole video
Which playlist contains this video?
how on 13:09 when we assume the variables independent many were 0 ??
Very nice lecture!
Thanks a lot sir.
Hello, the constant term in your example doesn't appear same to my solution.
what happens if the variables are dependent?
Why is sigma 12 =0. How to infer it from the scatter plot
05:10 it's σ 21 not σ12
Covariance of x1,x2 is same as covariance of X2,x1. so we can write σ 21 = σ12
How to find play list
Very helpful, thanks!
thank you very much.
nice explanation sir
Best tutorial :)
thank you
excellent
Unfortunately missed to explain the concept
sigma 21 not 12 D: if they are symmetric I guess it doesn't matter but for the sake of math write it right.
one year late, and don't remember this comment at all. D: if I was right I guess it doesn't matter but for the sake of the continuum time it right.
Doesn't matter sigma 12 will always be equal to sigma 21
👏😂😂 2 year late..now this comment won't be useful at all .but it will recall you that moment when you spend your time over this video
Have fun😂😂
Rakesh Rautela I will come back to comment on this next year.
I really appreciate this tutorial sir, if p=3 somebody should help me out
Please improve video quality
why sigma ,12 = 0? (6:25)
Hanzala Jamash, because, off diagonal elements in the matrix show covariance I.e how much they're dependent on each other... Since here he took example of independent variables covariance is zero hence sigma 12 is zero
Where is the 'sigma squared' at 10:13 coming from? Can anybody explain?
Sigma squared is nothing but Cov(X,X) in co variance matrix which equals to Var(X) . so for variable X1 its sigma1 squared and for variable X2 its sigma 2 squared
lost at 16:53
CLEANNNNNNNNNNNNNNNNNNN
11:34