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

  • @datamlistic
    @datamlistic10 ай бұрын

    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!

  • @Romba2020
    @Romba20203 ай бұрын

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

  • @datamlistic

    @datamlistic

    3 ай бұрын

    Thanks! Glad you liked it! :)

  • @koldengeese2214
    @koldengeese22144 ай бұрын

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

  • @datamlistic

    @datamlistic

    4 ай бұрын

    Glad it helped! :)

  • @catdog8751
    @catdog87516 ай бұрын

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

  • @datamlistic

    @datamlistic

    6 ай бұрын

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

  • @sumers9396
    @sumers93965 ай бұрын

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

  • @datamlistic

    @datamlistic

    5 ай бұрын

    Thanks a lot! Happy you liked it! :)

  • @ivanericsantosbergsten2761
    @ivanericsantosbergsten27613 ай бұрын

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

  • @prateekcaire4193
    @prateekcaire4193Ай бұрын

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

  • @datamlistic

    @datamlistic

    Ай бұрын

    Thanks! Glad you liked it! :)

  • @coolcalmnormal
    @coolcalmnormal Жыл бұрын

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

  • @datamlistic

    @datamlistic

    Жыл бұрын

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

  • @shreyaspakhare1313
    @shreyaspakhare13137 ай бұрын

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

  • @datamlistic

    @datamlistic

    7 ай бұрын

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

  • @realykid
    @realykidАй бұрын

    you are a great teacher, very intuitive explanation!!

  • @datamlistic

    @datamlistic

    Ай бұрын

    Thanks! Glad you liked the explanation! :)

  • @Jo30011
    @Jo30011Ай бұрын

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

  • @datamlistic

    @datamlistic

    Ай бұрын

    Glad it was helpful!:)

  • @pooper526
    @pooper5263 ай бұрын

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

  • @datamlistic

    @datamlistic

    3 ай бұрын

    Happy to hear that you liked it! :)

  • @harshalshedolkar4839
    @harshalshedolkar48399 ай бұрын

    Truly awesome presentation, Keep it up!!!

  • @datamlistic

    @datamlistic

    9 ай бұрын

    Thanks mate! Will do! :)

  • @iiVEVO
    @iiVEVO10 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

    @datamlistic

    10 ай бұрын

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

  • @pouyasojoudi3585
    @pouyasojoudi35856 ай бұрын

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

  • @datamlistic

    @datamlistic

    6 ай бұрын

    Thanks! Happy you liked it! :)

  • @Yozh2_
    @Yozh2_ Жыл бұрын

    Incredible explanation, thanks a lot!

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Thank you!!!

  • @anwmus
    @anwmus Жыл бұрын

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

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Glad it was helpful! :)

  • @shambo9807
    @shambo98077 ай бұрын

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

  • @datamlistic

    @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. :)

  • @sofia.cardenas.x
    @sofia.cardenas.x2 ай бұрын

    Thank you for your video!

  • @datamlistic

    @datamlistic

    2 ай бұрын

    Glad you liked it! :)

  • @anshumansharma2041
    @anshumansharma2041 Жыл бұрын

    what an amazing explanation!!

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Many thanks! Glad it was helpful!

  • @Blahcub
    @Blahcub5 ай бұрын

    Great explanation

  • @datamlistic

    @datamlistic

    5 ай бұрын

    Glad you liked it! :)

  • @cupq
    @cupq6 ай бұрын

    best video - huge respect

  • @datamlistic

    @datamlistic

    6 ай бұрын

    Many thanks! Glad you enjoyed it! :)

  • @user-ot2vx8pd5u
    @user-ot2vx8pd5u8 ай бұрын

    Thank you for this video

  • @datamlistic

    @datamlistic

    8 ай бұрын

    My pleasure! Happy you found it helpful! :)

  • @nihits
    @nihits8 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

    @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.

  • @user-ro1dr3hl4l
    @user-ro1dr3hl4l10 ай бұрын

    Thanks a lot for this intuitive explanation

  • @datamlistic

    @datamlistic

    10 ай бұрын

    Glad you enjoyed it! :)

  • @winwin-gw7rn
    @winwin-gw7rn5 ай бұрын

    Such a high quality content

  • @datamlistic

    @datamlistic

    5 ай бұрын

    Thanks! Glad you liked it! :)

  • @iacobsorina6924
    @iacobsorina6924 Жыл бұрын

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

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Thank you so much!!

  • @ahmedsoliman6167
    @ahmedsoliman61673 ай бұрын

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

  • @datamlistic

    @datamlistic

    3 ай бұрын

    Glad I could help! :)

  • @klevisimeri607
    @klevisimeri6076 ай бұрын

    Best video on youtu❤!

  • @datamlistic

    @datamlistic

    6 ай бұрын

    Thanks! Glad you think so! :)

  • @shaveddave4005
    @shaveddave4005 Жыл бұрын

    Awesome! Thank you

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Glad you found it helpful! :)

  • @atakan716
    @atakan7163 ай бұрын

    PERFECT!

  • @datamlistic

    @datamlistic

    3 ай бұрын

    Thanks! :)

  • @Alabsi3A
    @Alabsi3AАй бұрын

    Wow! Thank you

  • @datamlistic

    @datamlistic

    Ай бұрын

    You're welcome! :)

  • @AbhishekSinghSambyal
    @AbhishekSinghSambyalАй бұрын

    Beautiful.

  • @datamlistic

    @datamlistic

    Ай бұрын

    Thanks! :)

  • @buihung3704
    @buihung37047 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

    @datamlistic

    7 ай бұрын

    Glad to hear this explanation helped you! :)

  • Жыл бұрын

    This was awesome, thank you.

  • @datamlistic

    @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

    @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. :)

  • @fealgu100
    @fealgu100 Жыл бұрын

    Excellent!

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Many thanks!

  • @UdemmyUdemmy
    @UdemmyUdemmy Жыл бұрын

    BRAVO!!

  • @datamlistic

    @datamlistic

    Жыл бұрын

    Thank you!

  • @Elitea20
    @Elitea204 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

    @datamlistic

    4 ай бұрын

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

  • @enio9477
    @enio94777 ай бұрын

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

  • @datamlistic

    @datamlistic

    7 ай бұрын

    Thanks! I am happy you enjoyed it! :)

  • @user-nv3mc3zq3u
    @user-nv3mc3zq3u8 ай бұрын

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

  • @datamlistic

    @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. :)

  • @BilalAhmed-on4kd
    @BilalAhmed-on4kd3 ай бұрын

    why should the inflection point be at σ

  • @datamlistic

    @datamlistic

    3 ай бұрын

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

  • @RazingForx
    @RazingForx4 ай бұрын

    You deserve an accolade.

  • @datamlistic

    @datamlistic

    4 ай бұрын

    Thanks! :)

  • @spp626
    @spp6264 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

    @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

    @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

    @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

    @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!🙏🏻

  • @anngladyo5668
    @anngladyo56682 ай бұрын

    I broke my brain watching this

  • @datamlistic

    @datamlistic

    2 ай бұрын

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

  • @ahmedsoliman6167
    @ahmedsoliman61673 ай бұрын

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

  • @killxmen
    @killxmen4 ай бұрын

    God ………….

  • @vaibhavnakrani2983
    @vaibhavnakrani29832 ай бұрын

    Dude you are awesome! Keep it up. 🫡

  • @datamlistic

    @datamlistic

    2 ай бұрын

    Thanks! Will do! :)