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

[@datamlistic]

See how the Gaussian distribution is applied in practice for clustering: ua-cam.com/video/wT2yLNUfyoM/v-deo.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!

[@Romba2020]

Best intuitive explanation of normal distribution function, I have seen yet. Thanks a lot

[@datamlistic]

Thanks! Glad you liked it! :)

[@koldengeese2214]

Thank you very much. I never had any insight on what the numbers in the normal distribution formula meant until now.

[@datamlistic]

Glad it helped! :)

[@catdog8751]

Thanks so much, its amazing how you made something so intimidating so easy to understand

[@datamlistic]

Thanks! I am happy to hear that you enjoyed the explanation! :)

[@saifjawaid]

Only video I have ever watched in 0.75x. Such an amazing explanation. Thank you

[@datamlistic]

Thanks! Glad it was helpful! :)

[@ivanericsantosbergsten2761]

O cara é fera! Muito bom! Aula extraordinária!
Parabéns, professor!

[@sumers9396]

This video is a gem! Keep up the good work!

[@datamlistic]

Thanks a lot! Happy you liked it! :)

[@shreyaspakhare1313]

Awesome content !! A Lucid and easy to understand explanation for this topic. Thanks !

[@datamlistic]

Thank you so much! Glad to hear you found the explanation helpful and easy to understand! :)

[@coolcalmnormal]

Thanks a lot! This is awesome approach of explaining the concept in 7 mins!

[@datamlistic]

Thank you so much! I am glad you enjoyed it! :)

[@Jo30011]

Thank you so much for your great explanation! I´m so grateful you uploaded this video. 🙂💡

[@datamlistic]

Glad it was helpful!:)

[@prateekcaire4193]

Thanks a lot! Kudos to efforts you made to convey the meaning intuitively with wonderful animations

[@datamlistic]

Thanks! Glad you liked it! :)

[@pooper526]

This video makes it look so easy, especially the visualization of the graph.

[@datamlistic]

Happy to hear that you liked it! :)

[@harshalshedolkar4839]

Truly awesome presentation, Keep it up!!!

[@datamlistic]

Thanks mate! Will do! :)

[@realykid]

you are a great teacher, very intuitive explanation!!

[@datamlistic]

Thanks! Glad you liked the explanation! :)

[@Yozh2_]

Incredible explanation, thanks a lot!

[@datamlistic]

Thank you!!!

[@sofia.cardenas.x]

Thank you for your video!

[@datamlistic]

Glad you liked it! :)

[@anwmus]

Thank you very much for this video! Very clear explanation!

[@datamlistic]

Glad it was helpful! :)

[@shambo9807]

Very illustrative. Thank you. I might actually remember the formula now😅

[@datamlistic]

Thank you for tour feedback! I am happy to hear that this video helped you in better understading the multivariate normal distribution formula. :)

[@iiVEVO]

Best explanation I've seen. If you don't mind making a video on the univariate and multivariate GMM formula please :D

[@datamlistic]

Thank you! I am happy you enjoyed this explanation. :) I will add the two on my list of videos.

[@cupq]

best video - huge respect

[@datamlistic]

Many thanks! Glad you enjoyed it! :)

[@anshumansharma2041]

what an amazing explanation!!

[@datamlistic]

Many thanks! Glad it was helpful!

[@klevisimeri607]

Best video on youtu❤!

[@datamlistic]

Thanks! Glad you think so! :)

[@winwin-gw7rn]

Such a high quality content

[@datamlistic]

Thanks! Glad you liked it! :)

[@user-ot2vx8pd5u]

Thank you for this video

[@datamlistic]

My pleasure! Happy you found it helpful! :)

[@iacobsorina6924]

Very nice video. You are doing a good job! 🤗

[@datamlistic]

Thank you so much!!

[@user-ro1dr3hl4l]

Thanks a lot for this intuitive explanation

[@datamlistic]

Glad you enjoyed it! :)

[@Blahcub]

Great explanation

[@datamlistic]

Glad you liked it! :)

[@pouyasojoudi3585]

why can't professors explain like this?? great job bro!

[@datamlistic]

Thanks! Happy you liked it! :)

[@shaveddave4005]

Awesome! Thank you

[@datamlistic]

Glad you found it helpful! :)

[@atakan716]

PERFECT!

[@datamlistic]

Thanks! :)

[@Alabsi3A]

Wow! Thank you

[@datamlistic]

You're welcome! :)

[@AbhishekSinghSambyal]

Beautiful.

[@datamlistic]

Thanks! :)

[@ahmedsoliman6167]

thank you very musch you made my day ifront of my professor tarek

[@datamlistic]

Glad I could help! :)

[@fealgu100]

Excellent!

[@datamlistic]

Many thanks!

[@nihits]

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]

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.

This was awesome, thank you.

[@datamlistic]

Thanks mate! I am happy you enjoyed the explanation! :)

@@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]

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. :)

[@UdemmyUdemmy]

BRAVO!!

[@datamlistic]

Thank you!

[@buihung3704]

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]

Glad to hear this explanation helped you! :)

[@Elitea20]

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]

Wish you best of luck and I hope this video helped you to understand the maths behind the gaussian distribution! :)

[@enio9477]

Amazing explanation, thank you!
"I don't understand why it's such a big deal" hahaha

[@datamlistic]

Thanks! I am happy you enjoyed it! :)

[@RazingForx]

You deserve an accolade.

[@datamlistic]

Thanks! :)

[@user-nv3mc3zq3u]

why is e^x^2 at 0 giving a y value of 0, shouldnt it be 1?

[@datamlistic]

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. :)

[@BilalAhmed-on4kd]

why should the inflection point be at σ

[@datamlistic]

Tried my best to explain it at 2:42. :)

[@anngladyo5668]

I broke my brain watching this

[@datamlistic]

Sorry to hear that. Hope you're well. :(

[@spp626]

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]

Hey there! Not really sure where I am talking about the non-singular distribution. Could you point that out for me?

[@spp626]

@@datamlistic hello sir, actually I asked you a general doubt. This term is generally used with MND. Thats why I asked.

[@datamlistic]

​@@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]

@@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!🙏🏻

[@ahmedsoliman6167]

thank you very much you made me appear smart infront of my gf

[@killxmen]

God ………….

[@vaibhavnakrani2983]

Dude you are awesome! Keep it up. 🫡

[@datamlistic]

Thanks! Will do! :)