Multivariate Normal (Gaussian) Distribution Explained

Рет қаралды 28,184

Күн бұрын

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: 97

@datamlistic 11 ай бұрын

See how the Gaussian distribution is applied in practice for clustering: kzfaq.info/get/bejne/rbpirK9_uszdn4E.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 4 ай бұрын

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

@datamlistic 4 ай бұрын

Thanks! Glad you liked it! :)

@koldengeese2214 5 ай бұрын

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

@datamlistic 5 ай бұрын

Glad it helped! :)

@catdog8751 7 ай бұрын

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

@datamlistic 7 ай бұрын

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

@saifjawaid 23 күн бұрын

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

@datamlistic 23 күн бұрын

Thanks! Glad it was helpful! :)

@sumers9396 6 ай бұрын

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

@datamlistic 6 ай бұрын

Thanks a lot! Happy you liked it! :)

@ivanericsantosbergsten2761 4 ай бұрын

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

@coolcalmnormal Жыл бұрын

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! :)

@shreyaspakhare1313 8 ай бұрын

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

@datamlistic 8 ай бұрын

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

@pooper526 5 ай бұрын

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

@datamlistic 4 ай бұрын

Happy to hear that you liked it! :)

@Jo30011 2 ай бұрын

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

@datamlistic 2 ай бұрын

Glad it was helpful!:)

@realykid 2 ай бұрын

you are a great teacher, very intuitive explanation!!

@datamlistic 2 ай бұрын

Thanks! Glad you liked the explanation! :)

@iiVEVO 11 ай бұрын

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

@datamlistic 11 ай бұрын

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

@prateekcaire4193 2 ай бұрын

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

@datamlistic 2 ай бұрын

Thanks! Glad you liked it! :)

@harshalshedolkar4839 10 ай бұрын

Truly awesome presentation, Keep it up!!!

@datamlistic 10 ай бұрын

Thanks mate! Will do! :)

@Yozh2_ Жыл бұрын

Incredible explanation, thanks a lot!

@datamlistic Жыл бұрын

Thank you!!!

@anwmus Жыл бұрын

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

@datamlistic Жыл бұрын

Glad it was helpful! :)

@pouyasojoudi3585 7 ай бұрын

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

@datamlistic 7 ай бұрын

Thanks! Happy you liked it! :)

@sofia.cardenas.x 3 ай бұрын

Thank you for your video!

@datamlistic 3 ай бұрын

Glad you liked it! :)

@shambo9807 8 ай бұрын

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

@datamlistic 8 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. :)

@anshumansharma2041 Жыл бұрын

what an amazing explanation!!

@datamlistic Жыл бұрын

Many thanks! Glad it was helpful!

@cupq 7 ай бұрын

best video - huge respect

@datamlistic 7 ай бұрын

Many thanks! Glad you enjoyed it! :)

@iacobsorina6924 Жыл бұрын

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

@datamlistic Жыл бұрын

Thank you so much!!

@user-ro1dr3hl4l Жыл бұрын

Thanks a lot for this intuitive explanation

@datamlistic Жыл бұрын

Glad you enjoyed it! :)

@Blahcub 6 ай бұрын

Great explanation

@datamlistic 6 ай бұрын

Glad you liked it! :)

@user-ot2vx8pd5u 9 ай бұрын

Thank you for this video

@datamlistic 9 ай бұрын

My pleasure! Happy you found it helpful! :)

@winwin-gw7rn 6 ай бұрын

Such a high quality content

@datamlistic 6 ай бұрын

Thanks! Glad you liked it! :)

@shaveddave4005 Жыл бұрын

Awesome! Thank you

@datamlistic Жыл бұрын

Glad you found it helpful! :)

@klevisimeri607 7 ай бұрын

Best video on youtu❤!

@datamlistic 7 ай бұрын

Thanks! Glad you think so! :)

@ahmedsoliman6167 4 ай бұрын

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

@datamlistic 4 ай бұрын

Glad I could help! :)

@atakan716 4 ай бұрын

PERFECT!

@datamlistic 4 ай бұрын

Thanks! :)

@Alabsi3A 2 ай бұрын

Wow! Thank you

@datamlistic 2 ай бұрын

You're welcome! :)

@fealgu100 Жыл бұрын

Excellent!

@datamlistic Жыл бұрын

Many thanks!

@AbhishekSinghSambyal 2 ай бұрын

Beautiful.

@datamlistic 2 ай бұрын

Thanks! :)

@nihits 9 ай бұрын

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 9 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.

Жыл бұрын

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. :)

@UdemmyUdemmy Жыл бұрын

BRAVO!!

@datamlistic Жыл бұрын

Thank you!

@buihung3704 8 ай бұрын

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 8 ай бұрын

Glad to hear this explanation helped you! :)

@enio9477 8 ай бұрын

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

@datamlistic 8 ай бұрын

Thanks! I am happy you enjoyed it! :)

@Elitea20 5 ай бұрын

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 5 ай бұрын

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

@RazingForx 5 ай бұрын

You deserve an accolade.

@datamlistic 5 ай бұрын

Thanks! :)

@user-nv3mc3zq3u 9 ай бұрын

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

@datamlistic 9 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. :)

@anngladyo5668 3 ай бұрын

I broke my brain watching this

@datamlistic 3 ай бұрын

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

@spp626 5 ай бұрын

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 5 ай бұрын

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

@spp626 5 ай бұрын

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

@datamlistic 5 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 5 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!🙏🏻