Multivariate Normal (Gaussian) Distribution Explained
In this video I explain what the multivariate normal distribution (or the multivariate gaussian distribution) is, together with the meaning behind the equation that describes its behavior.
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Important Notes
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At 03:22 I forgot to add the dx to the integral... Whoopsie!
References
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Exponential function: • Exponential growth fun...
Deterimant: • The determinant | Chap...
Covariance Matrix: datascienceplus.com/understan...
Contents
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00:00 - Intro
00:18 - Exponential Functions
01:45 - Mean and Standard Deviation
02:40 - Finals Steps in Obtaining Normal Equation for 1-D
04:02 - Normalizing Term - Multivariate Normal Distribution
05:29 - Mean and Covariance Matrix - Multivariate Normal Distribution
06:52 - Outro
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#normaldistribution #multivariate #gaussian
Пікірлер: 95
See how the Gaussian distribution is applied in practice for clustering: kzread.info/dash/bejne/qYhm266Hhcnfn7A.html *Mistake notes* : Between 1:02 and 1:18, e^x^2 should be equal to 1 when x=0. Thanks @user-nv3mc3zq3u for noticing this!
Best intuitive explanation of normal distribution function, I have seen yet. Thanks a lot
@datamlistic
3 ай бұрын
Thanks! Glad you liked it! :)
Thank you very much. I never had any insight on what the numbers in the normal distribution formula meant until now.
@datamlistic
4 ай бұрын
Glad it helped! :)
Thanks so much, its amazing how you made something so intimidating so easy to understand
@datamlistic
6 ай бұрын
Thanks! I am happy to hear that you enjoyed the explanation! :)
This video is a gem! Keep up the good work!
@datamlistic
5 ай бұрын
Thanks a lot! Happy you liked it! :)
O cara é fera! Muito bom! Aula extraordinária! Parabéns, professor!
Thanks a lot! Kudos to efforts you made to convey the meaning intuitively with wonderful animations
@datamlistic
Ай бұрын
Thanks! Glad you liked it! :)
Thanks a lot! This is awesome approach of explaining the concept in 7 mins!
@datamlistic
Жыл бұрын
Thank you so much! I am glad you enjoyed it! :)
Awesome content !! A Lucid and easy to understand explanation for this topic. Thanks !
@datamlistic
7 ай бұрын
Thank you so much! Glad to hear you found the explanation helpful and easy to understand! :)
you are a great teacher, very intuitive explanation!!
@datamlistic
Ай бұрын
Thanks! Glad you liked the explanation! :)
Thank you so much for your great explanation! I´m so grateful you uploaded this video. 🙂💡
@datamlistic
Ай бұрын
Glad it was helpful!:)
This video makes it look so easy, especially the visualization of the graph.
@datamlistic
3 ай бұрын
Happy to hear that you liked it! :)
Truly awesome presentation, Keep it up!!!
@datamlistic
9 ай бұрын
Thanks mate! Will do! :)
Best explanation I've seen. If you don't mind making a video on the univariate and multivariate GMM formula please :D
@datamlistic
10 ай бұрын
Thank you! I am happy you enjoyed this explanation. :) I will add the two on my list of videos.
why can't professors explain like this?? great job bro!
@datamlistic
6 ай бұрын
Thanks! Happy you liked it! :)
Incredible explanation, thanks a lot!
@datamlistic
Жыл бұрын
Thank you!!!
Thank you very much for this video! Very clear explanation!
@datamlistic
Жыл бұрын
Glad it was helpful! :)
Very illustrative. Thank you. I might actually remember the formula now😅
@datamlistic
7 ай бұрын
Thank you for tour feedback! I am happy to hear that this video helped you in better understading the multivariate normal distribution formula. :)
Thank you for your video!
@datamlistic
2 ай бұрын
Glad you liked it! :)
what an amazing explanation!!
@datamlistic
Жыл бұрын
Many thanks! Glad it was helpful!
Great explanation
@datamlistic
5 ай бұрын
Glad you liked it! :)
best video - huge respect
@datamlistic
6 ай бұрын
Many thanks! Glad you enjoyed it! :)
Thank you for this video
@datamlistic
8 ай бұрын
My pleasure! Happy you found it helpful! :)
3:20 the inflection point is where the slop changes from concave to convex. Also at half height the width is 2.355 times and at 1/10 height it is 4.29 times. You can test it by giving 9 in the denominator making sigma as 3. the slope change happens at 3, its very subtle, at 1/2 height the width is 3*2.355=7.065 and at 1/10 height the width is 3*4.29=12.87.
@datamlistic
8 ай бұрын
Thanks for the feedback! I said in the video that at sigma and -sigma are inflection points. Also, the math you enumerated kinda checks out, but I am not sure how it relates to the usefulness of having the inflection points in sigma in -sigma.
Thanks a lot for this intuitive explanation
@datamlistic
10 ай бұрын
Glad you enjoyed it! :)
Such a high quality content
@datamlistic
5 ай бұрын
Thanks! Glad you liked it! :)
Very nice video. You are doing a good job! 🤗
@datamlistic
Жыл бұрын
Thank you so much!!
thank you very musch you made my day ifront of my professor tarek
@datamlistic
3 ай бұрын
Glad I could help! :)
Best video on youtu❤!
@datamlistic
6 ай бұрын
Thanks! Glad you think so! :)
Awesome! Thank you
@datamlistic
Жыл бұрын
Glad you found it helpful! :)
PERFECT!
@datamlistic
3 ай бұрын
Thanks! :)
Wow! Thank you
@datamlistic
Ай бұрын
You're welcome! :)
Beautiful.
@datamlistic
Ай бұрын
Thanks! :)
Holy f... I have learned statistics for a long time but nobody ever teach me the intuition behind probability distribution function. We just learn the formula and have zero knowledge about where does that formula come from?
@datamlistic
7 ай бұрын
Glad to hear this explanation helped you! :)
This was awesome, thank you.
@datamlistic
Жыл бұрын
Thanks mate! I am happy you enjoyed the explanation! :)
Жыл бұрын
@@datamlistic I particularly like how you include the animated parts which are great for building up intuition. Also just the right amount of density for my taste, with references to more rigorous materials. Way to go.
@datamlistic
Жыл бұрын
Thank you again for the feedback! Also, I would greatly appreciate if you could share with me your thoughts about what kind of subjects you would like to see on this channel. I am trying right now to collect new ideas about potential future videos. :)
Excellent!
@datamlistic
Жыл бұрын
Many thanks!
BRAVO!!
@datamlistic
Жыл бұрын
Thank you!
Guys im finished for my ML exam if he cant explain it to me god knows how I will understand this concept 😂 (great video its just that my mathematical background is a joke and my ML lecturer isn't helpful....)
@datamlistic
4 ай бұрын
Wish you best of luck and I hope this video helped you to understand the maths behind the gaussian distribution! :)
Amazing explanation, thank you! "I don't understand why it's such a big deal" hahaha
@datamlistic
7 ай бұрын
Thanks! I am happy you enjoyed it! :)
why is e^x^2 at 0 giving a y value of 0, shouldnt it be 1?
@datamlistic
8 ай бұрын
Yep, it should be 1 in x=0, my mistake and sorry if this confused you. I will add a pinned comment about this, so others know that this is an error from my side. Thanks for the feedback and please let me know if you find any other mistakes in this video or others that I've created. :)
why should the inflection point be at σ
@datamlistic
3 ай бұрын
Tried my best to explain it at 2:42. :)
You deserve an accolade.
@datamlistic
4 ай бұрын
Thanks! :)
Hello sir, I have a doubt. What is the meaning of non singular distribution? I am not getting the meaning of non singular there.
@datamlistic
4 ай бұрын
Hey there! Not really sure where I am talking about the non-singular distribution. Could you point that out for me?
@spp626
4 ай бұрын
@@datamlistic hello sir, actually I asked you a general doubt. This term is generally used with MND. Thats why I asked.
@datamlistic
4 ай бұрын
@@spp626 Well, I know what a stationary distribution means for Markov Chains - a distribution that remains unchanged in the Markov chain as time progresses. However, I am not sure how this would relate MND. Could you give me a little bit of context? Is this a general term that you encountered with MNDs?
@spp626
4 ай бұрын
@@datamlistic yes sir, I got the answer. Non singular distribution for MND is that for which the determinant of covariance matrix is non zero..Thank you so much sir for giving so much attention for my doubt. I am grateful to you!🙏🏻
I broke my brain watching this
@datamlistic
2 ай бұрын
Sorry to hear that. Hope you're well. :(
thank you very much you made me appear smart infront of my gf
God ………….
Dude you are awesome! Keep it up. 🫡
@datamlistic
2 ай бұрын
Thanks! Will do! :)