This explanation is amazing! Very clear 2D example which helps me conceptualize the Gaussian distribution in greater than 2 dimension. Thank you so much!
Very clear thanks a lot. I've seen this multi variate Guassians in my Bayesian ML course for a month now and I had no idea what the parameters do or how to visualise them. This video helped a lot.
I'd like to know how you call your x value for univariate case or x value set for multivariate case in your Gaussian distribuitons? Do you name them as "data set" or " variable set"? Also, what makes the mean value size same as the x data size? Thanks in advance. Should we think that we create a new mean average for every added x data point in our data set? That's why we average them when we find the best estimated value in the end.
In the formula at the minute 1.00, when you find the inverse of a Sigma matrix in the exp(...) , do you use unit matrix method, any coding , or some other method? Cheers.
Do you have an example of multivariate Gaussian with data set, for instance, thousands of values? I mean I have a histogram shaped like Gaussian, and it shows channel number on x axis and corresponding counts per channel on Y axis. How should be the equation? Can you refer Me a link or a book?
Hi Herman, best explanation ever! super helpful and inspiring of what you're doing here and slides as well. Would you be able to share with us the probability computation given by data in excel? kinda confused with how to multiply the covariance matrix by the (x - mean). thanks!
Hey a b! I'd definitely recommend watching these excellent videos: www.3blue1brown.com/topics/linear-algebra. They cover matrix multiplication in detail, and does so in a very intuitive way.
How do you call x, mu and sigma in likelihood function of a Gaussian distribution in statistics or in math (Variable, domain, data, parameter in univariate, bivariate, and multivariate case seperately) ? I am also asking this when there is only one data point or when you have a data set of x, when you have a vector of mean and sigmas, so on , so forth. Thanks in advance.
I would like to know how they are named in statistics. For instance, mu and sigma are called parameters; however x values can be called variables, arguments or a domain of a function, or maybe even a data point or a continuous data set.
If your x or mean vector is a row vector, then you cannot write the formula like at the minute of 1.06. It's because the transpose matrix of (x-mu) and the matrix of (x-mu) should be replaced. Transpose should be in the end, and (x-mu) should be in the begining.
Nice! If we were to simulate a Multivariate Gaussian distribution python, for example with cov = [1,2,1]. Do you know if that would be set as the row or the column? I mean, would that be the horizonal axis or vertical?
One more question about the example at the minute of 0.42, As far as I see, you can have 2 or more univariate formula coming from 2 x variable to create the multivariate case. When you combine them to see the combined likelihood, you have to have a mean vector in size of 2 or more as much as your data points of x concerns, and Sigma matrix will be the size of nxn if you had n x variable in your data set.. That's always the case, right? The size of the mean vector and the Sigma matrix are kind of defined by the number of combination of x values, righit?
Jip, that's exactly right: the dimensionality of the vector x (i.e. the number of scalar variables contained within x) determines the dimensionalities of the mean vector and covariance matrix. (And the shapes you give are correct.) I hope that also answers your other questions! :)
Best explanation of Multivariate Gaussian distribution I've seen so far. Hats off to you!
This is the first time to understand the covariance matrix! Thanks a lot for your time and effort!
This was the most helpful and concise explanation I could find on UA-cam. Thanks a lot! ❤
They say you don't understand something very well until you are able to simplify it. Well done!
This explanation is amazing! Very clear 2D example which helps me conceptualize the Gaussian distribution in greater than 2 dimension. Thank you so much!
Best explanation period. First one that made me understand the covariance matrix in the mvn
One of the best videos I've seen about multivariate gaussian distribution. Thank you!
Very clear thanks a lot. I've seen this multi variate Guassians in my Bayesian ML course for a month now and I had no idea what the parameters do or how to visualise them. This video helped a lot.
Great explanation
Simple, not fast, straight to the point
Why can't others do this?
perfect, to the point and explains the intuition. thank you!
Really clear and simple demonstrations. Thank you!
Big pleasure! :D
Very nice visual explaination. Thank you so much!
Best explanation with examples for multivariate gaussian
thats great explaination. people show formulas which scare me!!
ty
Thank you very much for this explanation!
Really nice explanation, and in just 5 mins!
You’re absolutely incredible I have yet to see a better vid in this subject
Thanks a ton! :D
Well done!
Thank you! I understand covariance better now
Wow. Thank you
Thanks!
I'd like to know how you call your x value for univariate case or x value set for multivariate case in your Gaussian distribuitons? Do you name them as "data set" or " variable set"? Also, what makes the mean value size same as the x data size? Thanks in advance. Should we think that we create a new mean average for every added x data point in our data set? That's why we average them when we find the best estimated value in the end.
Very clear explanation. Thanks
Thank you! :)
In the formula at the minute 1.00, when you find the inverse of a Sigma matrix in the exp(...) , do you use unit matrix method, any coding , or some other method? Cheers.
Do you have an example of multivariate Gaussian with data set, for instance, thousands of values? I mean I have a histogram shaped like Gaussian, and it shows channel number on x axis and corresponding counts per channel on Y axis. How should be the equation? Can you refer Me a link or a book?
amazing tutorial. Please, how can I contact you?
thx
Could you also tell us how to get the sigma (covmatrix) in the first place from a fit information on a data? Cheers.
Have a look at this video: ua-cam.com/video/i6Rp0eiINgM/v-deo.html
Hi Herman, best explanation ever! super helpful and inspiring of what you're doing here and slides as well. Would you be able to share with us the probability computation given by data in excel? kinda confused with how to multiply the covariance matrix by the (x - mean). thanks!
Hey a b! I'd definitely recommend watching these excellent videos: www.3blue1brown.com/topics/linear-algebra. They cover matrix multiplication in detail, and does so in a very intuitive way.
@@kamperh hi this is super helpful! I am taking this course now, it will surely fill the foundation gap I have. :)
How do you call x, mu and sigma in likelihood function of a Gaussian distribution in statistics or in math (Variable, domain, data, parameter in univariate, bivariate, and multivariate case seperately) ? I am also asking this when there is only one data point or when you have a data set of x, when you have a vector of mean and sigmas, so on , so forth. Thanks in advance.
I would like to know how they are named in statistics. For instance, mu and sigma are called parameters; however x values can be called variables, arguments or a domain of a function, or maybe even a data point or a continuous data set.
If your x or mean vector is a row vector, then you cannot write the formula like at the minute of 1.06. It's because the transpose matrix of (x-mu) and the matrix of (x-mu) should be replaced. Transpose should be in the end, and (x-mu) should be in the begining.
Absolutely correct! Fortunately I use column vectors in all these videos, so then everything is correct.
Nice! If we were to simulate a Multivariate Gaussian distribution python, for example with cov = [1,2,1]. Do you know if that would be set as the row or the column? I mean, would that be the horizonal axis or vertical?
What exactly do you mean with cov = [1,2,1]? Maybe more concretely: how many variables are you modelling here?
One more question about the example at the minute of 0.42, As far as I see, you can have 2 or more univariate formula coming from 2 x variable to create the multivariate case. When you combine them to see the combined likelihood, you have to have a mean vector in size of 2 or more as much as your data points of x concerns, and Sigma matrix will be the size of nxn if you had n x variable in your data set.. That's always the case, right? The size of the mean vector and the Sigma matrix are kind of defined by the number of combination of x values, righit?
Jip, that's exactly right: the dimensionality of the vector x (i.e. the number of scalar variables contained within x) determines the dimensionalities of the mean vector and covariance matrix. (And the shapes you give are correct.) I hope that also answers your other questions! :)
@@kamperh Could you please also comment on the question below? Cheers.