Logistic Regression - THE MATH YOU SHOULD KNOW!

[@Actanonverba01]

Love the math full proofs! That stuff is rarely shown even in classes. There is just not enough time to... Great stuff!

[@SpecialBlanket]

Yup. I came here after staring at Bishop (the book) for 3 hours failing to get through some of the "trivial" skipped steps.

[@mktsp2]

Yeah, most statistics lecturers are loosers

[@UnPuntoyComa]

This is the most clearly explained and well developed video about the issue I have seen. Most explanations stop with the maximization of the log likelihood function, and I couldn't find how it is maximized until now. I didn't understand a bit, but it's better to know that something is beyond my comprehension than not knowing what it is. Thank you! Subscribed.

[@nikoczernin]

I've learned this that uni a dozen times, never truly got it though. You made it click for me, thank you!

[@kevinshao9148]

THE BEST only 9 min to illustrate Logistic Regression! Really appreciate your brilliant work!

[@oksaubercool]

Very good explanation. Only thing, you're starting really slow, which is perfect, but then when the math gets messy you speed up by 10 times and go by without further explanations. Nonetheless very useful.

[@calluma8472]

Yeah anyone who can follow the maths at that speed doesn't need this video I think.

[@andyd568]

Just pause the video and look up the terms he mentions. I think the problem is if he stops to go into each subtopic the video would become a lecture unto itself.

[@95Bloulou]

I disagree, I think the speed is really nice during the whole video because it is calculus details that you can study if you want by just pausing the video.

[@SpecialBlanket]

I disagree. Toward the end he's just rearranging the equations.

[@UnPuntoyComa]

I also considered the speed was adequate. I simply couldn't follow after he mentioned "Taylor series" just because I don't have a clue of what that is, but I get that what he did, if I knew about numerical methods wouldn't be so complicated.

[@jerrylu532]

Oh man, you just saved my course project! Thanks for these great help that really explained how the math works!

[@qingli1799]

Amazing! Parameter estimation in logistic regression has confused me for so long. I know MLE is used to estimate betas in logistic regression. However, the full math proofs really clarify the way! Really appreciate your video!

[@mohammedismail308]

Sometimes the good demonstration is nothing without such one example which is deploying the theory in practice. Thanks at all :)

[@bambinodeskaralhes]

Thank you very much !!!! The only guy who could make me understand this subject !!!! You are great !!!!!!

[@chriskong7418]

Love the maths part. Definitely my hero in ML.

[@haifasaud1001]

Yesssssss finally! No one ever gives any significance into the mathematical part

[@christophersolomon633]

I find this a really nice video which strikes a good balance between general principles and details (which can be a very tricky thing to do). I had spent some time reading a textbook about the method and had a few uncertainties. This seemed just the ticket to clarify it all.

[@dm3248]

After going through so many videos, finally understood. Thanks!!

[@haraldurkarlsson1147]

Excellent! Clear and logical explanation of all the steps involved.

[@Trakushun]

Clear explanation and in deep developed. Charming voice and very good structure. Thanks dude!

[@professorg000]

Excellent job --- congratulations. You sound about 15 years old!!! Even more impressive

[@haojiang4882]

Dude you killing it! Best explanation +1!

[@haojiang4882]

Subed!

[@CodeEmporium]

Thanks a ton! Glad to have you on board! Made a similar video on Kernelisation (and the kernel trick) yesterday. Check it out!

[@haojiang4882]

@@CodeEmporium Absolutely!

[@hikmatullahmohammadi27]

Thank you for crystal clear explanations.

[@basantmounir]

Can someone please explain at 5:20 how did we convert the expression into a summation? And how was the log part of the new expression of summation? Also, what do the s and n in the counters represent and is there a relationship between them? Thank you.

[@dominiccordeiro9257]

you take the log of a product. Then convert it to sums of logs. for example: log (a*b) = log(a) + log(b)

[@romanwang7562]

I was able to implement this with a minor difference: I used X.T instead of X for the middle term inside the weight update expression

[@stephanschaefer155]

Thank very much. First time I understand how the coefficients sre calculsted. Great!

[@CraftyChaos23]

07:54 In gradiant of loss function equation there should be X instead of XT

[@vivian_who]

Excellent video!!! I have been looking for something exactly like this... Thanks!

[@CodeEmporium]

Awesome! Very welcome!

[@Saravananmicrosoft]

Very good explanation, i did that step by step derivative with your material can you do video on maths involved for backward propagation

[@Ltsoftware3139]

From what I understand, by estimating the beta parameter, we only determine the slope of the sigmoid, but it is still centered on the x-axis. My data is only positive, so in my case, I need another parameter to shift the whole sigmoid to the left or right.

[@9181shreyasbhatt]

u mean by using e^-(beta0 + beta1 x) instead of e^-(beta1 x) in sigmoid function

[@hnkulkarni]

Thank you for this explanation.

[@sahilchaturvedi593]

Best explanation on youtube. Thanks :)

[@CodeEmporium]

Glad it was useful! :)

[@marx427]

Omg i was looking for this ! ❤️

[@binyillikcinar]

Decent but NewtonRaphson is not the only numerical method. It could be better to list few alternatives, especially Gradient-Descent to the top of the list. Since it involves single derivative the parameter update rule is much simpler.

[@kkkk150984]

How the powers come yi and 1-yi at 5:19 in video please clarify..

[@giacomopauletti5099]

I am watching the video rn ... did you find the answer to your question? If you did, pls tell me the answer because I have been struggling from such a long period

[@Ltsoftware3139]

For the part p(xi)^yi -> if yi = 1 we will remain with p(xi), but if yi=0 that element will not have any impact. For the second part (1-xi)^(1-y1) it's exactly the opposite. If yi = 1 then we will have (1-xi)^0, so the term will not have any impact. If yi=0 then we will have (1-xi)^1=1-xi. Basically, raising to the power of yi filters(get's rid of) all the elements where yi=0, and raising to the power of (1-yi) filters all the elements where yi=1.

[@dm3248]

@@Ltsoftware3139 thanks!!

[@maryamrastegar6368]

thank you. it was very helpful in my exam.

[@mridulavijendran3062]

why do we maximize the product(in particular) of the probabilities? Is it to exploit the idea that the log of the products are sums and it could also help simplify the calculations of the sigmoid function? Edit: How do we know that P(1-P) is a diagonal matrix?

[@name6297]

The explanation was really good. Can you suggest a couple of math courses that help better visualize what I've seen here?.Thanks :-)

[@rocavincent2266]

At 6:25, I think there is a sign error for the calculus of beta_{t+1}. You make a subtraction as in gradient descent, whereas we want to maximize the likelihood here. Am I right ?

[@Tyokok]

Great explain in such short 9 min. Subscribed! One question: in your video, you finally got formula beta(t+1) = beta(t) + ......., so how you set up beta(t=0) the initial value of beta to start your iteration? Thank you very much in advance!

[@CodeEmporium]

Thanks for hopping board! You can randomly initialize your parameters ( the beta vector ).

[@Tyokok]

@@CodeEmporium I see. Many thanks for the reply!

[@Tyokok]

@@deepanshudashora5887 hope it's not too late if you ask me or the poster. linear regression for linear model predict a value, logistic regression for classification problem.

[@vaishanavshukla5199]

very simplified and good explaination

[@user-xt9js1jt6m]

Nice info. How do we obtain standard errors of estimators in logistics regression?? Kindly guide me

[@Tyokok]

Dear Sir, if I may have 2 questions here: 1) 7:25, how did you remove y_i as it's independent? yi can be opposite signs, how can it be removed like 1? 2) at 7:58 in matrix representation why you convert p(x_i) in different way? or it really doesn't matter, cuz you will substitute beta_i in sigmoid function at each iteration? Many Thanks!

[@Actanonverba01]

Hey, do you have a book reference for the math you show here? Awesome work! :)

[@henrychen1544]

Hi, I was wondering where the term yi came from and what do you mean by s in yi thank you

[@moisessoto5061]

Can we do a linear regresion of the logit to the explanatory variables and get the probabilities from the fitted logit?

[@CodeEmporium]

Linear regression expects the outcome y to be continuous - not categorical

[@yulinliu850]

Excellent! Thanks a lot!

[@vaishanavshukla5199]

great explaination !!!!!

[@rithealeang6217]

Don’t quite understand when you said remove y as it is independent to beta and no gradient term with p(x)x. Any explanation thank

[@juntong8488]

Thanks, very clear.

[@areejnasser6664]

Great explanation

[@bevansmith3210]

one word: thankyou!

[@PCD1387]

can you please tell which book do you follow ?

[@sijiahuang6936]

Hi, I just want to ask, in the last formula, should it be "X^T" instead of "X"? I mean the middle "X" in (X^T * W*X)^(-1) X (Y-Y').

[@shardx191]

i dont understand at 4:40 , what does s in yi=1 means ? how does it relate to the P notation

[@mahammadodj]

it means the independent variable is 1 in dataset.

[@cuysaurus]

at 8:21 is it X^T (Y-Yhat^(t)) instead of X(Y-Yhat^(t))? in the very last line.

[@ssshukla26]

Yes.

[@aayusmaanjain9854]

Can someone please explain why the yi and (1-yi) term goes to the exponent in the second equation when we combine the product at 5:20

[@CodeEmporium]

We took the logarithm of the equation. A property of logarithms is the exponent term can be written as a product. And we took the logarithm in the first place since we want to just find the betas that maximize the value of L. The values of betas remain the same if we maximize the log of the equation too (a property called “monotonically increasing functions”)

[@mahammadodj]

Could anyone explain why P(1-P) is written as W at 8:12 ?

[@1UniverseGames]

What will happen if we use (-1,1) instead of (0,1) in logistic function, what kind of equations it will give? Any video or source to study this?

[@विशालकुमार-छ7त]

1/(1+e^(-bx)) always lie between 0 and 1. There is no choice to use anything, the function is chosen in such a way that it always lie between 0 and 1.

[@akshatjain1699]

hey, i am having difficulty in implementing the formula in python. the matrix inside the inverse bracket is singular matrix. how do I solve this

[@hayatt143]

Awesome Explanation. I was looking for an answer to this question. Please help. In Logistic Model ,a coefficient has value 1.6. This means that each unit change in the corresponding predictor variable multiples the odds of the outcome by how much?

[@sominya]

e^1.6

[@hayatt143]

can you give the formula to calculate this..? coz options are a) 2.75 b)3.95 c)4.75 d)4.95

[@malepatirahul7339]

in loglikelihood function how was the seventh step calculated

[@shivampradhan6101]

I watched the whole playlist but didn't understand much of the maths.what should I do

[@musarratazim7940]

Why you don't estimate alpha? ?you only consider Beta in logistic regression model

[@CodeEmporium]

Sorry. What is alpha in this case?

[@musarratazim7940]

In logistic regression parameter alpha is also also present (book gujrati econometrica and walepole introduction to statistics) but in this case why you not take it.

[@animeshsharma7332]

7:38 from where that goddamn transpose arrived

[@CheetahDFurious20]

Hi.. Actually In terms of matrix we cannot multily any matix by itself as such i.e. if you consider X is a matrix and if you want to calculate X * X then we cannot do it as such because order of matrix i.e. m x n wont allow us untill and unless it is sqaure matix else we have to transpose it and then multiply it.. X (m x n) * X ^T (n x m) = XX^T (m x m). Hope this final representation would help you... Thanks Happy learning...

[@sorvex9]

@@CheetahDFurious20 Thanks bro

[@hareedyhareedy2863]

Can you please create another with examples

[@shubhijain2706]

Please someone help me with this, I am lil confused whether Y hat at 7:54 and P at 7:58 are same?

[@AlexSmith-tr9hc]

"Numerically encoding classes looses meaning" - looses? Did you mean "loses" at 0:31?

[@CodeEmporium]

Yeah. "loses" is right. My bad

[@mkaberli]

You could drop the music.

[@JDMathematicsAndDataScience]

Great. I’ve never heard of this pronunciation of matrix.

[@bin5156]

It was sooo helpful!

[@CodeEmporium]

Glad is was!

[@oluwole635]

Please I have a presentation on logistic regression and the part of the Hessian Matrix where we applyed the gradient, can someone please explain to me. I got all other thing including the matrices but only that. Please help ASAP.

[@shahnawazfingertips5367]

dude we can use gradient descent instead of newton raphson

[@himeshph]

Hidden gem

[@anverHisham]

Thanks a lot :-)

[@CodeEmporium]

Super welcome!

[@user-xt9js1jt6m]

Wt if there are two parameter? Alpha and beta??

[@ColinXYZ]

You’d just do the same steps, but derive for your other variable instead .

[@utkarshsingh2675]

perfecto!

[@rishhabhnaik2298]

How did we remove yi at 7:27 ?

[@ssshukla26]

yi is independent of beta.

[@tasnimyusof7079]

Hi, could you share also if there are few variables.. How to get every coefficient for the variable.. Let say it have 5 variables. Thankssss 😁

[@ltbd78]

Thanks

[@azaira010]

20 times speedy lecture for me..... i am a noob in deep learning

[@nebiyathawi7457]

hello,its is nice man

[@louerleseigneur4532]

merci

[@kumaravelk1091]

Content is good... but going too fast..

[@CodeEmporium]

Kumaravel K thanks for the feedback. I'll pace myself better in future videos

[@faisalsal1]

The background music is distracting.

[@farooq8fox]

I lost it at 5:50, Ill comeback when im smarter

[@ninjawarrior_1602]

Bro not a worry see until that moment he has just simplified the equation and now he just want to maximise the function Additionally Then he is using Taylor's series expansion and truncating that to two terms

[@Dave-nz5jf]

lol it's loses not looses.

[@Felicidade101]

if you are here I recommend you check out this video too, kzbin.info/www/bejne/r3q8fIVqqMytf5o its from StatsQuest. Super good channel.

[@Areeva2407]

You are a Good Tutor but content is very Basic .. No Solved Examples ,,, Purpose not solved. Please also add Learning Outcomes at the beginning so that we can save our time.

[@rohanreddymelachervu3498]

Why video in chinese??