Linear Regression from a Probabilistic Perspective | Deriving the Least Squares Loss

[@MachineLearningSimulation]

Errata: At 5:53 in the probability density function of the Gaussian: I missed the square on the sigma. The correct prefactor in the exponential would be 1/(2 * sigma²). It is fixed in the PDF on GitHub: github.com/Ceyron/machine-learning-and-simulation/blob/main/english/probabilistic_machine_learning/linear_regression_univariate_intro.pdf Thanks to @Numi for pointing this out :)

[@felix6027]

I have been trying to wrap my head around this concept. I have seen a lot of other videos on this topic, But only your explanation made perfect sense to me. Thank for this! You just gained a subscriber!

[@MachineLearningSimulation]

Thanks a lot

[@alaanasser3243]

I am new to the topic of simulation in general but I find you content a thing of beauty. Thanks for offering this on KZbin.

[@MachineLearningSimulation]

You're very welcome ☺️ Welcome to the channel ❤️

[@mpost909]

Doing my master in datascience after being a total math noob. Your video's are the best at intuitively explaining (probabilistic) ML on the platform and making me believe that I can get this degree! Thanks!

[@MachineLearningSimulation]

Wow, thanks! :) These are such nice words. I am extremely happy to help. Especially, since I know that my teaching might be a little bit unconventional in some regards. 😅

[@shajidmughal3386]

thanks, feel like i know regression better now than ever

[@MachineLearningSimulation]

Nice 😊 I'm glad, I could help 👍

[@parthbatra99]

Looking at your choices of keyboard, phone and framework laptop, good job mate. We need more informed consumers like you. I myself imported framework laptop in India last year because of the same reasons

[@MachineLearningSimulation]

Nice :D How do you like your framework so far? My XPS is now ~4 years old. Probably, I will keep it for two more years and then it's going to be the 2nd gen of Framework.

[@parthbatra99]

@@MachineLearningSimulation I bought the windows one. It's the only laptop I have outside my job so use it mostly for side projects and entertainment. It's been working flawlessly as of now. No heating issues, no glitches, very good performance, no driver issues. However I would have loved a better webcam and speakers. But it's the best part that I can replace these.

[@MachineLearningSimulation]

@@parthbatra99 That sounds great. :)

[@minglee5164]

such an insightful perspective

[@MachineLearningSimulation]

Thanks 🙏 glad you liked it.

[@circuit-me]

Yet another awesome video. I have one question, at 7:40 - when computing likelihood of data why conditional probability P(Y|X) is used why not joint probability P(Y, X) = P(Y|X)* P(X)?

[@krishnabhogaonker3368]

Here are just my two cents. So in graphical models we are usually looking for the joint distribution as you suggest, where Z is the set of unknown variables and the set X is usually known data. So in many bayesian books you will see the joint distribution P(Z, X=D), where D is the data. This formulation is also described as P(Z | X = D), since we know the values of X, and that reduces the distribution of the unknowns Z. So in Bayesian regression--in particular in this video, the unknown is the slope "M". So we could also say that we are looking for the distribution of M given the data. So that would be something like P(M, X, Y) as the joint probability, or P(M | X, Y) since we have observed both X and Y--and we are really interested in the distribution of M.

[@EngRiadAlmadani]

hi great work is there any text book about these topics

[@MachineLearningSimulation]

Hi, thanks for the kind words :) I can recommend "pattern recognition and machine learning" by Christopher Bishop. It's a tough read, but definitely worth it.

[@ahmedsuliman9067]

Thanks

[@MachineLearningSimulation]

You're welcome 🤗

[@xxish123]

Really good

[@MachineLearningSimulation]

Thanks a lot ☺️

[@OdhranOC]

My apologies for the unrelated question. Do you by any chance have any example of implementing Crank Nicholson in Python in any of your videos?

[@MachineLearningSimulation]

Hi, no problem regarding the question ;) Unfortunately, there is no such video yet. There is the plan to have a series on Numerical Methods for PDEs that goes into high detail. In this series, I am also planning to cover Crank Nicholson but it will probably take me some more time since I first want to finish some other Playlists.

[@OdhranOC]

@@MachineLearningSimulation looking forward to it!

[@MachineLearningSimulation]

@@OdhranOC Nice :)

[@OdhranOC]

@@MachineLearningSimulation out of curiosity are you an academic researcher? Physics or engineering? Engineering background cfd researcher I suppose?

[@MachineLearningSimulation]

@@OdhranOC I just recently finished my Master Degree in Computational Science and Engineering. Prior to that, I did Mechanical Engineering. Though, I love Math and Computer Science and teaching :D. I hope the latter is noticeable throughout the channel. Feel free to connect on LinkedIn if you want: www.linkedin.com/in/felix-koehler/ ☺

[@saeednuman]

I think inside exponential you will have 1/2*Sigma^2, the square is missing. Thanks for the informative video

[@MachineLearningSimulation]

Hi, thanks for spotting the error. You are absolutely right. :) I fixed it in the PDF on GitHub (github.com/Ceyron/machine-learning-and-simulation/blob/main/english/probabilistic_machine_learning/linear_regression_univariate_intro.pdf ) and left a pinned comment and a note inside the video. :D Gladly, it does not affect the further derivation 😁

[@saeednuman]

@@MachineLearningSimulation Yes, it didn't affect the result. You are doing a great job; thanks.

[@MachineLearningSimulation]

@@saeednuman Thanks a lot for the feedback, ♥ I really appreciate it.

[@saeednuman]

I have a short question, which book do you mainly refer to for fundamental machine learning topics?

[@MachineLearningSimulation]

​@@saeednuman From a theoretical perspective, I like Bishop's "Pattern Recognition and Machine Learning". However, it is really tough. It took me over three years to (almost fully) read it. There are still sections I have not touched yet. Kevin Murphy's "Machine Learning: A Probabilistic Perspective" is also nice. At some points it goes even deeper than Bishop's. These are extremely hard books, :D. Don't be intimidated. Though, they are amazing resources. For an easier approach, check out "An introduction to statistical learning". And of course, there are many hands-on books. Personally, I like Aurelien Gerons books.

[@philipp5636]

Haha wtf you are my age but light years smarter than me! Are you creating this videos while working full time?

[@MachineLearningSimulation]

Thanks :D. I mean, I love teaching, and it helps me better understanding the topics when I have to explain them. At the moment, I am in a transitioning phase before my PhD starts.

[@shankerram3]

bruh going 100mph . dotn forget to breathe bruh

[@MachineLearningSimulation]

Haha :D Yes, that's one of the earlier videos. The pacing of my voice should be better in the newer vids.