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Machine Learning | Gradient Descent (with Mathematical Derivations)

  Рет қаралды 101,298

RANJI RAJ

RANJI RAJ

Күн бұрын

Пікірлер: 150
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
For notes👉 github.com/ranjiGT/ML-latex-amendments
@sudiptodas6272
@sudiptodas6272 3 жыл бұрын
What is great about this particular video is these concepts are explained well in many places like scattered dots , you connected the dots to paint the whole picture . an example for gradient descent included - very helpful .
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
Thank You for your valuable feedback 😊
@gabelster3729
@gabelster3729 Жыл бұрын
You just helped me understand hundreds of web pages that talked about topics with no order. Thank you
@donaldngwira
@donaldngwira 2 жыл бұрын
You are such a great teacher. Concepts are clearly explained beginning with the basics and slowly easing into the most advanced level. Thank you
@RanjiRaj18
@RanjiRaj18 2 жыл бұрын
You're very welcome!
@subramaniarumugam6902
@subramaniarumugam6902 2 жыл бұрын
My god you are perfect I think your work should reach more audience your best and clear than the renowned ML yputubers. Applause Ranji
@yashdhawade5341
@yashdhawade5341 7 ай бұрын
The best and clear explanation I've ever listened about Gradient Descent. Keep up the good work!🙌
@RanjiRaj18
@RanjiRaj18 7 ай бұрын
Awesome, thank you!
@aryandeshpande1241
@aryandeshpande1241 2 жыл бұрын
this might be the most underrated explanation on youtube
@rajapal9736
@rajapal9736 3 жыл бұрын
Hi, Your video is helpful for beginners to understand the concept. One suggestion: In the very beginning of the video when you write the equation of your predicted line remember to mark it as y(cap) = mx(i) + c. It is not y(i) which is the actual data point.
@amarnammilton
@amarnammilton 9 ай бұрын
its a very good description, The way you teach is humble and appreciatable.
@RanjiRaj18
@RanjiRaj18 9 ай бұрын
Thank you very much!
@kvv6671
@kvv6671 9 ай бұрын
When my ML teacher teaching this , I felt I am learning some rocket science ,but you are teaching it felt very easy , thank you Sir😊
@RanjiRaj18
@RanjiRaj18 9 ай бұрын
Glad to hear that
@chinmaysrivastava3212
@chinmaysrivastava3212 5 ай бұрын
I was unable to understand this topic tried many videos but this was the most useful video thankss
@vedanthbaliga7686
@vedanthbaliga7686 3 жыл бұрын
This is what I pay my internet bill for! Thanks a lot!
@sumanmondal5276
@sumanmondal5276 4 жыл бұрын
Your hard work made the concept very easy to grasp. Kudos.......
@Sagar_Tachtode_777
@Sagar_Tachtode_777 2 жыл бұрын
Everything is so easy on this channel, great work Man!
@RanjiRaj18
@RanjiRaj18 2 жыл бұрын
Glad you like them!
@swaroopthomare7237
@swaroopthomare7237 Жыл бұрын
Hey thank you so much for this content since I started studying regression using your videos , I became huge fan of yours
@RanjiRaj18
@RanjiRaj18 Жыл бұрын
Thank you for your comment. Glad you like it ;)
@alhassanturay7233
@alhassanturay7233 8 ай бұрын
Truest your the best. You solve my long time machine learning challenge.
@manishjain9703
@manishjain9703 Жыл бұрын
I am a beginner and as a beginner I was struggling understand the gradient decent concept. I have seen many videos on gradient decent however all of them skipped explaining the derivative part however you explained it very well both (total and partial) with solution . Thanks!
@RanjiRaj18
@RanjiRaj18 Жыл бұрын
Great to hear!
@vishaldas6346
@vishaldas6346 4 жыл бұрын
Man, you've won my heart, you kept it so simple, best way of explaining Gradient Descent. Can you please help me in using learning rate in the equation and number of steps used in gradient descent with an example.
@theysigankumar1671
@theysigankumar1671 3 жыл бұрын
Sir thank you very much, this has been so helpful since my course will only get tougher from here onwards and u helped me understand the basics
@maneetsaluja
@maneetsaluja Жыл бұрын
Great explanation with an example. This is the way to explain such concepts.
@RanjiRaj18
@RanjiRaj18 Жыл бұрын
Thank you for the comment. Happy Learning!
@classy_Girl8920
@classy_Girl8920 Жыл бұрын
perfect video for core concept understanding , amazing.. I love the explanation.. thankyou so much
@tusharsub1000
@tusharsub1000 2 жыл бұрын
As far as I know, gradient descent doesn't talk about solving 'm' and 'c' directly by putting them into two equations like the way you did it here..Because sometime the expression that we get after differentiation becomes so complex especially with logistic regression, random forest and other complex model in deep learning that solving 'm' and 'c' directly becomes extremely tricky and time complexity becomes very high...So Gradient descent talks about solving 'm' and 'c' by some trial and test method. Starting with some dummy value of 'm' and 'c' and putting those values in the equation of differentiation and check if the value of differentiation(say D0) for those 'm' and 'c' becomes 0 or close to 0. If not, then subtract that differentiation value(D0) from the old value of 'm' and 'c' and get a new 'm' and 'c' and again check if the value of differentiation (say D1) for those new 'm' and 'c' comes close to 0. Continue like this till you find that old 'm' - value of differentiation is very very close to 0. That 'm' becomes your actual 'm' and similarly the same thing to be done for 'c'.
@RanjiRaj18
@RanjiRaj18 2 жыл бұрын
This video was an intuitive way for understanding gradient descent for beginners. Anyways appreciate your time to quote about your understanding of GD.
@ArunKumar-yb2jn
@ArunKumar-yb2jn 2 жыл бұрын
@@RanjiRaj18 Good explanation. I think you have shown derivation for Ordinary Least Squares method. As far as Machine Learning is concerned it has to be slightly adapted.
@maxpatrickoliviermorin2489
@maxpatrickoliviermorin2489 Жыл бұрын
He solved m and c in this case because it wasn't a very complex example. Only one independent variable. In a multiple linear regression it would have been much more complex.
@jayaprakashs4412
@jayaprakashs4412 5 ай бұрын
Very good explanation. It would've been good if you could've explained the usage of learning rate usage to find a minimum point.
@sonnyarulanandam
@sonnyarulanandam 2 ай бұрын
Very good explanation of gradient descent
@shaun2201
@shaun2201 3 жыл бұрын
Hi @ranjiraj , at 21:37 u have given a wrong explanation in the partial derivative w.r.t C... d/dC (-C) will be -1 ,then why are you treating it as constant whereas in d/dc mx should be taken as constant.
@BADURELGADIR-dd2ck
@BADURELGADIR-dd2ck 2 ай бұрын
simple and useful lecture.. thanks
@RanjiRaj18
@RanjiRaj18 2 ай бұрын
You are welcome
@sundar8147
@sundar8147 11 ай бұрын
Thanks for the clear explanation sir
@lingadevaruhp5576
@lingadevaruhp5576 5 ай бұрын
Really amazing, thank you so much sir, keep rocking
@RanjiRaj18
@RanjiRaj18 5 ай бұрын
Always welcome
@trendhindifacts
@trendhindifacts 4 ай бұрын
Well explained bro ❤ just bring another video for statistics and linear algebra 🎉
@bhamidimaharshi
@bhamidimaharshi 27 күн бұрын
explanation is simply awesome.....
@Rambabukatta-ox6tc
@Rambabukatta-ox6tc 4 ай бұрын
very nicely explained Bro
@RanjiRaj18
@RanjiRaj18 4 ай бұрын
Glad you liked it
@vigneshwar2897
@vigneshwar2897 6 ай бұрын
will the sign ( direction ) for calculating m and b at last change, from addition to subtraction if we take "y-pred - y" instead of "y - y-pred" lke you have done in cost function ? i saw at few articles where this was mentioned but it was not clear.
@MrAmarSindol
@MrAmarSindol 2 жыл бұрын
killer explanation !! amazingly amazing !! thank you bro
@anushadevi4937
@anushadevi4937 3 жыл бұрын
Thank you so much, I got a clear picture of the topic now.
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
You are welcome!
@vasachisenjubean5944
@vasachisenjubean5944 3 жыл бұрын
you earned a subscriber my man
@anarkaliprabhakar6640
@anarkaliprabhakar6640 Жыл бұрын
sir u explained so well
@Shivendra7277
@Shivendra7277 2 жыл бұрын
Thankyou sir , Make more videos on machine learning concepts .
@Venomus658
@Venomus658 3 жыл бұрын
Thank you! Wish me luck on exam about it!
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
Good Luck 👍
@OpeLeke
@OpeLeke 2 жыл бұрын
excellent video
@RajSingh-ik3og
@RajSingh-ik3og 2 ай бұрын
great explainnation
@aaryan3461
@aaryan3461 2 жыл бұрын
Great video man. Loved it.
@manasagowrikottur8242
@manasagowrikottur8242 4 жыл бұрын
Thanks for this tutorial sir..made it very easy and simple.
@sherifbadawy8188
@sherifbadawy8188 2 жыл бұрын
one of the best
@suhasrewatkar9001
@suhasrewatkar9001 Ай бұрын
Best explanation sir
@salmansayyad4522
@salmansayyad4522 3 жыл бұрын
Thanks a lot sir! It was really helpful. Excellent explaination.
@pursuitofgrowthwithtr
@pursuitofgrowthwithtr 4 жыл бұрын
your videos are really nice, good content and presentation...keep it up sir.
@helloworld2740
@helloworld2740 2 жыл бұрын
really nice approch to teach thank you sirji
@danielsehnoutek2016
@danielsehnoutek2016 3 ай бұрын
Absolutely the best explanation
@danielsehnoutek2016
@danielsehnoutek2016 3 ай бұрын
If I got it your last example is analytical solution, but it couldn't been done everytime, then we use iterative solution with alpha learning rate?
@sanusimuhammad7466
@sanusimuhammad7466 9 ай бұрын
i have this video over and over again, it the most satisfying video i have seen, in as much as gradient decent is concer, but i have questions, 1 what happen to the 2 tha became the multiple of the function as chain rules implies, then what happen to the no in the cost function. i know its mean squared errored thing. in my small assumption either of the values cant be thrown away just like that mathematically. please help with explanation.
@1234wellwell
@1234wellwell 3 жыл бұрын
Thanks so much for the video. It helped me a lot.
@patelraj3140
@patelraj3140 4 жыл бұрын
Thank you so much sir for such a perfect explanation....🙏🙏👏👏👏
@dheerajverma189
@dheerajverma189 2 ай бұрын
Sir linear regression is not used for classification as you said in satrting of video while explaining
@SrikantBhusan
@SrikantBhusan 4 ай бұрын
between the timestamp 21:39 to 21:45 you told that partial derivative of y(i)-mx-c with respect to c is 0 so only take minus sign which is wrong it will be -1 because of here c is not constant.
@shivammodi1105
@shivammodi1105 3 жыл бұрын
Lovely explanation
@sarasijbasumallick4036
@sarasijbasumallick4036 2 жыл бұрын
can you please tell me why the curve is much sharp when you draw the graph with respect to j and c ? please tell
@user-dd7el9dp3d
@user-dd7el9dp3d Ай бұрын
At 20.37, you discarded n/2. I would like to know why?
@mahmoodapurbo5537
@mahmoodapurbo5537 7 ай бұрын
Thanks bro.
@umermehboob5630
@umermehboob5630 3 жыл бұрын
That is a explanation. I have one question, where would the learning rate be actually used in computation. Like in your numerical example. We found the outputs and calculated corresponding m and c. How does the learning rate is catered. Secondly, when we multiply learning rate with derivative, what does it gives us ?
@nileshpandey5724
@nileshpandey5724 2 жыл бұрын
thank you so much sir
@debrajnath6031
@debrajnath6031 3 жыл бұрын
The explanation of mathematical formula is absolutely fantastic. The explanation was about with single feature. But if we have multiple feature, what to be changed in the equation? Can you please let us know that. Thanks very much, and we will love to see this kind of videos shortly.
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
In case of multiple features or weights we have to conisder them individually by taking the partial derivtaive. This video is just a general idea of gradient descent. Hope it answers your question.
@Nudaykumar
@Nudaykumar 4 жыл бұрын
Hi one question here: First derivative: xsquare =2x Second derivative = 2 ( replaced in same location) Third derivative = 0 While applying same in mean square error formula First derivative= I understood square to 2/n(•••) Second derivative: with respective to slope It should be 2/n I=1 to n (yi -xi -c) here I applied second derivative replacing. Since -mxi converts to -xi. But In ur explanation instead of replacing, you brought second derivative to starting as below: 2/n I= 1 to n -xi(yi-mxi-c) In the same way for intercept. One more At the end , what happened to 2/n? Please correct me if I am wrong.
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
2/n Σi=1 to n -xi(yi-mxi-c) this comes from chain rule watch this part carefully again in the video, this (y-mxi-c) is the result of (yi-mxi-c)^2 and now since we want to differentiate wrt to slope m again you take the derivative now you treat the y and c as constants and what's left is -mxi so you get -xi that's what you get and you multiply with this(y-mxi-c). 2/n is a constant say for any number, n=5; 2/5 =constant you eventually equate it to zero so it vanishes away. Hope now you understand!
@mihirnaik3383
@mihirnaik3383 2 жыл бұрын
Thanks Buddy :)
@praveenkumar-nh5qs
@praveenkumar-nh5qs 4 жыл бұрын
Nicely explained.
@RahulTiwari-oe1ww
@RahulTiwari-oe1ww 2 жыл бұрын
Well explained
@testenma5155
@testenma5155 4 жыл бұрын
Hi Ranji Sir, i have a doubt. In 17:00 you have mentioned that we need to take derivative because we have two variables. And mentioned variables as x and c. But I think you were supposed to say m and c. later in 17:27 you mentioning about two parameters m and c. Please verify whether it correct or not. If i have pointed out wrong please apologize me.
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
Yes you are correct we have to take derivative wrt m and c
@ramnarayan3323
@ramnarayan3323 3 жыл бұрын
Thanks ...very well explained
@nightsky5037
@nightsky5037 Жыл бұрын
why do we set the derivative equal to 0? i mean the gradient at the minima might not be equal to zero for all curves
@mayank265memories
@mayank265memories 3 жыл бұрын
Amazing lecture. x^n, will not have a 3rd order derivate to be 0, it will be n+1 order derivate.
@ayushsingh-qn8sb
@ayushsingh-qn8sb 3 жыл бұрын
great explaination
@aerogrampur
@aerogrampur 3 жыл бұрын
keep up the good work !
@mariawilson6807
@mariawilson6807 4 жыл бұрын
Sir my maths is quite weak i want to start my career in data science i know that i can make my math strong but how should i start to learn maths for data science
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
Hello Maria, you can refer to websites like www.mathsisfun.com/ to learn the basics. Hope it helps!
@mariawilson6807
@mariawilson6807 4 жыл бұрын
@@RanjiRaj18 thanks sir
@mariawilson6807
@mariawilson6807 4 жыл бұрын
@@RanjiRaj18 Sir its very low level mathematics I am in sybsc it
@dineshlogu9368
@dineshlogu9368 3 жыл бұрын
can you please explain me why we are squaring the step at 4.36 . everything is clear to me except this one squaring step I cant able to understand..
@suryakrishna760
@suryakrishna760 Жыл бұрын
What should i do if i am to apply learning rate of some value?
@fpl8648
@fpl8648 3 жыл бұрын
thank you!!!
@fpl8648
@fpl8648 3 жыл бұрын
It was very helpful, in writing a thesis. Could you also indicate some bibliography for citations
@chaithanyack
@chaithanyack 3 ай бұрын
What type is it batch gradient?
@aqharinasrin7002
@aqharinasrin7002 Жыл бұрын
dear sir, I still cannot connected what is the purpose we do m = m - lambda * dJ/dm and c = c - lambda * dJ/dC
@leninfonseca7129
@leninfonseca7129 Жыл бұрын
Yess .. exactly....plz explain the proof of these 2 equations
@AdityaSingh-lf7oe
@AdityaSingh-lf7oe 4 жыл бұрын
Hi Ranji sir, I wanted to ask that if there are if our line is of the form M1*(feature1) + M2*(feature2).... Mn*(feature n) + c, do we have to follow same steps and calculate dJ/dm for all M1, M2...Mn?
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
Yes, one by one
@rameshthamizhselvan2458
@rameshthamizhselvan2458 4 жыл бұрын
Excellent...
@apoorva3635
@apoorva3635 2 жыл бұрын
Why do we need partial derivative when we have the total derivative?
@RanjiRaj18
@RanjiRaj18 2 жыл бұрын
When there are relatively larger coefficients in your model, taking total derivate would be a diffuícult task and also to estimate the optimal parameter. Partial derivatives reduces the workload by keeping one parameter as constant and determine the other.
@iramarshad700
@iramarshad700 3 жыл бұрын
So gradient descent is our cost function to calculate the error
@laodrofotic7713
@laodrofotic7713 3 жыл бұрын
J = 1/(2*m) * sum (h(x)-y)^2. being h(x) the hipotesis and y the accurate value... at 3:37 you got them mixed up right? damn man.. no wonder people get confused
@pavankumar8673
@pavankumar8673 2 жыл бұрын
Linear regression for classfication at 0:20???
@dineshlogu9368
@dineshlogu9368 3 жыл бұрын
Thanks you so much but I have small clarification regarding differentiate. why we are differentiate with respect to m , c & why we should not differentiate with respect to x to find out the value of y..
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
Because m, c are the weights that we want to determine which will give the best equation for curve fitting.
@dineshlogu9368
@dineshlogu9368 3 жыл бұрын
@@RanjiRaj18 thanks you so much for spending time to respond to my comment..
@sudhansumtripathy
@sudhansumtripathy Жыл бұрын
hi, sir do you have the python code using tensor flow or do you have any recordings of ML using TF
@OpeLeke
@OpeLeke 2 жыл бұрын
can this method work for an equation with multiple slopes?
@testenma5155
@testenma5155 4 жыл бұрын
How did the 2/n gone from equation when dJ/dm and dj/dc was assigbed to 0
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
2/n is a constant say you take n =5 so it becomes 2/5 so it's derivative is zero
@testenma5155
@testenma5155 4 жыл бұрын
@@RanjiRaj18 Thank you Ranji
@sandhu6355
@sandhu6355 Жыл бұрын
bro please ans this question why we are taking summation of c in one equation and not in other ---> one is 5C why
@sandhu6355
@sandhu6355 Жыл бұрын
Plase ans
@sirajmotaung6930
@sirajmotaung6930 3 жыл бұрын
Thank you so much..quick question, when/how do we use the learning rate in this regard?
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
If I understood your question correctly then: When? learning rate is made use for convergence, it should not be neither too large nor too low just optimal, so that your traning process is complete. How? You can use learning rate schedule or can use optimizers like ADAM.
@sirajmotaung6930
@sirajmotaung6930 3 жыл бұрын
@@RanjiRaj18 Yes, Alright thank you so much. Your vid was really helpful.
@suryatej839
@suryatej839 2 жыл бұрын
is it a sweet, in the middle of a hyperplane?
@tonmoy2431
@tonmoy2431 4 жыл бұрын
thank you sir
@mohamedelbatoty
@mohamedelbatoty 3 жыл бұрын
Thanks Bro :)
@viddeshk8020
@viddeshk8020 2 жыл бұрын
🙂👍 nice like that
@abhiaaron1715
@abhiaaron1715 Жыл бұрын
why at the end multiply the 2 nd equation with 5
@RanjiRaj18
@RanjiRaj18 Жыл бұрын
To make equation balance on both sides for cancellation. Those are basic algebraic rules.
@divyamohan6113
@divyamohan6113 4 жыл бұрын
thanks a lot..... :)
@mariawilson6807
@mariawilson6807 4 жыл бұрын
Which level of maths is required 11th and 12th or degree level mathematics ?
@RanjiRaj18
@RanjiRaj18 4 жыл бұрын
Personally both Derivatives, differential equations, Matrices and vector concepts
@mariawilson6807
@mariawilson6807 4 жыл бұрын
@@RanjiRaj18 thanks
@mohdhashim2321
@mohdhashim2321 4 жыл бұрын
sir explane krne ke baad thoda side ho jaya kijiye screenshot lena rehta hai
@shafiqahmad9057
@shafiqahmad9057 3 жыл бұрын
Sir can you recommend a book for machine learning with mathematical background please
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
You can refer the book by `Tom Mitchell`
@shafiqahmad9057
@shafiqahmad9057 3 жыл бұрын
@@RanjiRaj18 sir please what is book name and if you share pdf link it will be better
@RanjiRaj18
@RanjiRaj18 3 жыл бұрын
@@shafiqahmad9057 You can check on google it is open source
@shafiqahmad9057
@shafiqahmad9057 3 жыл бұрын
@@RanjiRaj18 thank you for very fast respomse
@someshh7263
@someshh7263 2 жыл бұрын
Sorry bro, Not clear what you saying..
@manashalder3999
@manashalder3999 4 жыл бұрын
havoc explanation
@mondal1839
@mondal1839 2 жыл бұрын
Doesn't he look like Bharati's (a comedian on Kapil Sharma's show) husband?😅
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