Multivariate Normal (Gaussian) Distribution Explained

[@datamlistic]

See how the Gaussian distribution is applied in practice for clustering: kzbin.info/www/bejne/rYWVqn-Eisuspa8 The covariance matrix video is out. Check it out here: kzbin.info/www/bejne/m5y9gqeelqilnLc *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! :)

[@woomy_squid]

Как же долго я искал адекватное объяснение многомерного нормального распределения! При этом, пришлось принять одномерное распределение таким, какое оно есть, без доказательств. Я искал серебро, а нашел золото! Объяснение, которое мои преподаватели так старательно избегали, уместилось в 7-минутное видео и 1 шортс. Спасибо за сохраненные время, нервы и веру в себя. Вы лучшие!

[@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! :)

[@zefmgamer3843]

You have no idea how much I appreciate you. Thank you so much, you made these unintuitive-looking equations make so much sense.

[@datamlistic]

You're very welcome! Glad it helped! :)

[@sacado42]

you're 100 times better then all the professors I've ever had thank you for you video

[@datamlistic]

Thanks! Glad you enjoyed the explanation! :)

[@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! :)

[@sumers9396]

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

[@datamlistic]

Thanks a lot! Happy you liked it! :)

[@nicolaihornung3625]

You should make videos like this professionally for educational institutions or simply directly for students on KZbin. This is exactly the kind of educational material I'd want. Really good job! To be particular I REALLY enjoy how you keep looping through different parameters for the particular element of the distribution you're discussing so one gets a clear idea of how different input affects the function. Thanks for this!! Also good job keeping the slides simple, having timestamps on the video and no unimportant 'bla bla' information - right to the bone! (unlike StatQuest who wastes so much time singing, saying BAM, trying to emotionally support me through his videos saying something will be hard but to hang on etc.....). Again, very well done!😀

[@datamlistic]

Thanks! Glad you liked the explanation! :)

[@saifjawaid]

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

[@datamlistic]

Thanks! Glad it was helpful! :)

[@yhbarve]

This is insanely good explanation!

[@datamlistic]

Thanks! Glad you think so! :D

[@pouyasojoudi3585]

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

[@datamlistic]

Thanks! Happy you liked it! :)

[@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! :)

[@ivanericsantosbergsten2761]

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

[@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.

[@thomasbates-km4ms]

You have understanding, my friend! Thank you for this video!

[@datamlistic]

Thanks! Glad it was helpful! :)

[@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.

[@AshishRaj04]

This video is a gem

[@datamlistic]

Thanks!

[@michaelmuller136]

Precise and easy to understand, thank you!

[@datamlistic]

Thanks! Glad you found the explanation that way! :)

[@prateekcaire4193]

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

[@datamlistic]

Thanks! Glad you liked it! :)

[@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. :)

[@realykid]

you are a great teacher, very intuitive explanation!!

[@datamlistic]

Thanks! Glad you liked the explanation! :)

[@harshalshedolkar4839]

Truly awesome presentation, Keep it up!!!

[@datamlistic]

Thanks mate! Will do! :)

[@samas69420]

3:18 i think that the reason of the factor 1/2 in the exponent is that when you compute the variance of the distribution you get exactly sigma^2, if you use the first distribution without 1/2 you get that the variance is sigma^2/2 and maybe this is not ideal when you need to work with it

[@Yaira-b2p]

Thank you so much, this vide is so undervalued

[@datamlistic]

Thanks!🙏

[@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! :)

[@anshumansharma2041]

what an amazing explanation!!

[@datamlistic]

Many thanks! Glad it was helpful!

[@Jo30011]

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

[@datamlistic]

Glad it was helpful!:)

[@newbie8051]

Had to calculate the entropy of a multivariate gaussian in my PRML midsem, wow The prof really likes multivariate gaussian, he even asked it in the Intro to DL course endsem (back in the 4th semester of my undergrad)

[@datamlistic]

Hehe, I also had a prof back in my masters that was obsessed with eigenvalues and eigenvectors. Anyway, I hope this video made you better understand the multivariate gaussian distribution. :)

[@Yozh2_]

Incredible explanation, thanks a lot!

[@datamlistic]

Thank you!!!

[@ahmedsoliman6167]

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

[@datamlistic]

Glad I could help! :)

[@klevisimeri607]

Best video on youtu❤!

[@datamlistic]

Thanks! Glad you think so! :)

[@winwin-gw7rn]

Such a high quality content

[@datamlistic]

Thanks! Glad you liked it! :)

[@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! :)

[@waisyousofi9139]

very intuitive explanation. Can you please let us know, where can we interact with that visualization?

[@datamlistic]

Well, I've written them in Python when I created them. Not really sure if I still have them, but I can check out ideas you're still interested.

[@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! :)

[@anwmus]

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

[@datamlistic]

Glad it was helpful! :)

[@12kenbutsuri]

Very nice summary! I have a question, I sometimes see this curly N notation. Is that like a simplified notation of this?

[@datamlistic]

Curly N is the notation for the normal distribution. :)

[@JitendraNathNaik-p9u]

Thanks a lot for this intuitive explanation

[@datamlistic]

Glad you enjoyed it! :)

[@iacobsorina6924]

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

[@datamlistic]

Thank you so much!!

[@Blahcub]

Great explanation

[@datamlistic]

Glad you liked it! :)

[@sofia.cardenas.x]

Thank you for your video!

[@datamlistic]

Glad you liked it! :)

[@emirbfitness]

Thank you very much

[@datamlistic]

Any time! :)

[@Lilk-m7d]

Thank you for this video

[@datamlistic]

My pleasure! Happy you found it helpful! :)

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. :)

[@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! :)

[@23232323rdurian]

thank you. that was great

[@datamlistic]

Thanks! Glad it was helpful! :)

[@shaveddave4005]

Awesome! Thank you

[@datamlistic]

Glad you found it helpful! :)

[@atakan716]

PERFECT!

[@datamlistic]

Thanks! :)

[@zhizhongpu8937]

v. helpful thanks!

[@datamlistic]

Glad it was helpful! :)

[@fealgu100]

Excellent!

[@datamlistic]

Many thanks!

[@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!🙏🏻

[@AbhishekSinghSambyal]

Beautiful.

[@datamlistic]

Thanks! :)

[@BilalAhmed-on4kd]

why should the inflection point be at σ

[@datamlistic]

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

[@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. :)

[@RazingForx]

You deserve an accolade.

[@datamlistic]

Thanks! :)

[@Alabsi3A]

Wow! Thank you

[@datamlistic]

You're welcome! :)

[@ahmedsoliman6167]

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

[@anngladyo5668]

I broke my brain watching this

[@datamlistic]

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

[@AnjaneeKumar-g4t]

excellent

[@datamlistic]

Thanks!

[@UdemmyUdemmy]

BRAVO!!

[@datamlistic]

Thank you!

[@vaibhavnakrani2983]

Dude you are awesome! Keep it up. 🫡

[@datamlistic]

Thanks! Will do! :)