Bayesian Linear Regression : Data Science Concepts 

As soon as you explained the results from Bayesian my jaw was wide open for like 3 minutes this is so interesting

Read it on a book. Didn't understand jack shit back then. Your videos are awesome. Rich, small, consise. Please make a video on Linear Discriminant Analysis and how its related to bay's theorem. This video will be saved in my data science playlist.

This video is a true gem, informative and simple at once. Thank you so much!

Love you, bro, I got my joining letter from NASA as a Scientific Officer-1, believe me, your videos always helped me in my research works.

Regardless of how they were really initially devised, seeing the regularization formulas pop out of the bayesian linear regression model was eye-opening - thanks for sharing this insight

For me, the coolest thing about statistics is that every time I do a refresh on these topics, I get some new ideas or understandings. It's lucky that I came across this video after a year, which could also explain why we need to "normalized" the X (0 centered, with stdev = 1) before we feed them into the MLP model, if we use regularization terms in the layers.

This is my favorite video out of a large set of fantastic videos that you have made. It just brings everything together in such a brilliant way. I keep getting back to it over and over again. Thank you so much!

Best of all videos on Bayesian regression; other videos are so boring and long but this one has quality as well as ease of understanding..Thank you so much!

This is incredible. Clear, well paced and explained. Thank you!

Really good explanation. I really like how you gave context and connected all topics together and it make perfect sense. While maintaining the perfect balance b/w math and intution. Great worl. Thank You !

Brilliant and clear explanation, I was struggling to grasp the main idea for a Machine Learning exam but your video was a blessing. Thank you so much for the amazing work!

Man I'm going to copy-paste your video whenever I want to explain regularization to anyone! I knew the concept but I would never explain it the way you did. You nailed it!

Man! What a great explanation of Bayesian Stats. It's all starting to make sense now. Thank you!!!

Your videos are great. Love the connections you make so that stats is intuitive as opposed to plug and play formulas.

Unbelievable, you explained linear reg, explained in simple terms Bayesian stat, and showed the connection under 20min .... Perfect

I've seen everything in this video many, many times, but no one had done as good a job as this in pulling these ideas together in such an intuitive and understandable way. Well done and thank you!

Thanks, man. A really good and concise explanation of the approach (together with the video on Bayesian statistics).

Your videos are a true gem, and an inspiration even. I hope to be as instructive as you are if I ever become a teacher!

Excellent tutorial! I have applied RIDGE as the loss function in different models. However, it is the first time I understand the mathematical meaning of lambda. It is really cool!

Awesome explanation! Especially the details on the prior were so helpful!

I used to be afraid of Bayesian Linear Regression until I saw this vid. Thank you sooo much

Amazing video! Really clearly explained! Keep em coming!

This video is super informative! It gave me the actual perspective on regularization.

Super informative and clear lesson! Thank you very much!

Amazing, you kept it simple and showed how regularization terms in linear regression originated from Bayesian approach!! Thank U!

Cristal clear! , thank you so much, the explanation is very structured and detailed

Thank you for this amazing video, It clarified many things to me!

This is truly cool. I had the same thing with the lambda. It’s good to know that it was not some engineering trick.

It just blown my mind too. I can feel you brother. Thank you!

This was an excellent introduction to Bayesian Regression. Thanks a lot!

This is sooo clear. Thank you so much!

This video is amazing!!! so helpful and clear explanation

very cool the link you explained between regularization and prior

Mi mente explotó con este video. Gracias

Thanks a lot! Great! I am reading Elements of Statistical Learning and did not understand what they were talking about. Now I got it.

Love this content! More examples like this are appreciated

This was incredible, thank you so much.

Awesome explanation!

Awesome video. I didn't realize that the L1, L2 regularization had a connection with the Bayesian framework. Thanks for shedding some much needed light on the topic. Could you please also explain the role of MCMC Sampling within Bayesian Regression models? I recently implemented a Bayesian Linear Regression model using PyMC3, and there's definitely a lot of theory involved with regards to MCMC NUTS (No U-Turn) Samplers and the associated hyperparameters (Chains, Draws, Tune, etc.). I think it would be a valuable video for many of us. And of course, keep up the amazing work! :D

This was awesome, thanks a lot for your time :)

Thanks, that was a good one. Keep up the good work!

Incredible explanation!

you got a subscriber, awesome explanation. I spent hours learning it from other source, but no success. You are just great

This is brillian man! Brilliant! Literally solved where the lamda comes from!

You are a great teacher thank you for your videos!!

Thanks for video.. Its really helpful.. I was trying to understand how regularization terms are coming.. Now i got. Thanks ..

Your videos are a Godsend!

At last!! I could find an explanation for the lasso and ridge regression lamdas!!! Thank you!!!

at last!!! Now I can see what lamda was doing in tne lasso and ridge regression!! great video!!

truly excellent explanation; well done

This blew my mind.Thanks

This is an awesome explanation

Thank you for sharing this fantastic content.

Thanks a lottttt! I had so much difficulty understanding this.

you are so good at this, this video is amazing

Tks a lot for this clear explanation !

This is the best explanation of L1 and L2 I've ever heard

You are the go-to for me when I need to understand topics better. I understand Bayesian parameter estimation thanks to this video! Any chance you can do something on the difference between Maximum Likelihood and Bayesian parameter estimation? I think anyone that watches both of your videos will be able to pick up the details but seeing it explicitly might go a long way for some.

thank you so much for the great explanation

Wow, killer video. This was a topic where it was especially nice to see everything written on the board in one go. Was cool to see how a larger lambda implies a more pronounced prior belief that the parameters lie close to 0.

Great video with a very clear explanation. COuld you also do a video on Bayesian logistic regression

wonderful stuff! thank you

Thank you very much. Pretty helpful video!

Can you please please do a series on categorical distribution, multinomial distribution, Dirichlet distribution, Dirichlet process and finally non parametric Bayesian tensor factorisation including clustering of steaming data. I will personally pay you for this. I mean it!! There are a few videos on these things on youtube, some are good, some are way high-level. But, no one can explain the way you do. This simple video has such profound importance!!

Mind blown on the connection between regularization and priors in linear regression

perfect explanation thank you

There is an error at the beginning of the video, in frequentist approaches X is treated as non random covariate data and y is the random part so the high variance of OLS should be expressed as small changes to y => big changes to OLS estimator. The changes to covariate matrix becoming big changes to OLS estimator is more like a non robustness of OLS wrt outlier contamination. Also the lambda should be 1/2τ^2 not σ^2/τ^2 since: ln(P(β))=-p * ln(τ * √2*π) - ||β||₂/2τ^2 Overall this was very helpful cheers!

What a wonderful explanation!!

Most insightful! L1 as Laplacian toward the end was a bit skimpy, though. Maybe I should watch your LASSO clip. Could you do a video on elastic net? Insight on balancing the L1 and L2 norms would be appreciated.

Notes for my future revision. *Priror β* 10:30 Value of Prior β is normally distributed. The by product of using Normal Distribution is Regularisation. Because the prior values of β won't be too large (or too small) from the mean. Regularisation keep values of β small.

such a nice explanation. I mean thats the first time I actually understood it.

Great video, do you have some sources I can use for my university presentation? You helped me a lot 🙏 thank you!

Thank You , I saw this before but i didnt understand. Please , where can i find the complete derivation? And maybe You can do a complete series in this topic

Legendary video

You are THE LEGEND

Great video!!

I'd never considered a Bayesian approach to linear regression let alone its relation to lasso/ridge regression. Really enlightening to see!

Great video. The relation between the prior and LASSO penalty was a "wow" moment for me. It would be helpful to see actual computation example in python or R. A common problem I see in Bayesian lectures is - too much focus on math rather to show how actually/ how much the resulting parameters differs. Specially, when to consider bayesian approach over ols.

At the end I understand it too finally. A hint for peaple who also struggle on BR like me: do a Bayesian linear regression in Python from any tutorial that you find online, you are going to understand, trust me. I think that one of the initial problems for a person that face a Bayesian approach it’s the fact that you are actually obtaining a posterior *of weights*!. Now looks kinda obvious but at the beginning I was really stuck, I could not understand what was actually the posterior doing.

Excellent thank you

fantastic! u r my savor!

thank you so much for this

Great thanks! .. was feeling the same discomfort about the origin of these...

Nice i never thought that 👍🏼👍🏼

very great, thank you

your videos are awesome so much better than my prof

you are a great teacher!!!🏆🏆🏆

Thank you very much

Excellent

Amazing! But where did Ridge and Lasso start from? Were they invented with Bayesian statistics as a starting point, or is that a duality that came later?

Holy shit! This is amazing. Mind blown :)

Max ( P(this is the best vid explaining these regressions | RU-vid) )

Beautiful!

thank you!

I wonder if this is related to BIC, Bayesian Information Criterion. It's about choosing the simpler model with fewer variables, similar to regularization.

Wonderfully explained! Mathematicians should be more subscribed to!

Excellent!

Great video. A quick question though. If we consider (beta) belonging to a N(0, t^2), how do we explain why beta can't be zero in case of Ridge?

mind boggling

Great video, just a question, where can I get some example of the algebra?