Mathematics for Machine Learning Tutorial (3 Complete Courses in 1 video)

TIME STAMP IS IN COMMENT SECTION
For a lot of higher level courses in Machine Learning and Data Science, you find you need to freshen up on the basics in mathematics - stuff you may have studied before in school or university, but which was taught in another context, or not very intuitively, such that you struggle to relate it to how it’s used in Computer Science. This specialization aims to bridge that gap, getting you up to speed in the underlying mathematics, building an intuitive understanding, and relating it to Machine Learning and Data Science
At the end of this specialization you will have gained the prerequisite mathematical knowledge to continue your journey and take more advanced courses in machine learning.
⭐ Important Notes ⭐
⌨️ This course is created in collaboration with Imperial college London
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[@MyLesson007]

------------ TIME STAMP ------------- In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. COURSE 1 MATHEMATICS FOR MACHINE LEARNING:LINEAR ALGEBRA INTRODUCTION TO LINEAR ALGEBRA AND TO MATHEMATICS FOR MACHINE LEARNING 0:00:00 Introduction Solving data science challenges with mathemaatics 0:02:27 Motivations for linear algebra 0:05:57 Getting a handle on vectors 0:15:03 Operations with vectors 0:26:32 Summary VECTORS ARE OBJECTS THAT MOVE AROUND SPACE 0:27:37 Introduction to module 2 - Vectors 0:28:27 Modulus & inner product 0:38:28 Cosine & dot product 0:44:21 Project 0:51:09 changing basis 1:02:34 Basis, Vector space, and linear independence 1:06:47 Application of changing basis 1:10:16 Summary MATRICES IN LINEAR ALGEBRA:OBJECTS THAT OPERATE ON VECTORS 1:11:36 Matrices, Vectors, and solving simultaneous equation problems 1:17:08 How matrices transform space 1:22:49 Types of matrix transformation 1:31:28 Composition or combination of matrix transformations 1:40:28 Solving the apples and bananas problem Gaussian elimination 1:48:29 Going from Gaussian elimination to finding the inverse matrix 1:57:07 Determinants and inverses 2:07:44 Summary MATRICES MAKE LINEAR MAPPINGS 2:08:43 Introduction Eintein summation convention and the symmetry of the dot product 2:18:37 Matrices changing basis 2:29:52 Doing a transformation in a changed basis 2:34:30 Orthogonal matrices 2:41:10 The Gram-Schmidt process 2:47:18 Example Reflecting in a plane EIGENVALUES AND EIGENVECTORS:APPLICATION TO DATA PROBLEMS 3:01:28 Welcome to Module 5 3:02:20 What are eigenvalues and eigenvectors 3:06:45 Special eigen-cases 3:10:17 Calculating eigenvectors 3:20:25 Changing to the eigenbasis 3:26:17 Eigenbasis example 3:33:43 Introduction to PageRank 3:42:27 Summary 3:43:42 Wrap up of this linear algebra course ---------------------------------------------- The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. Course 2 MULTIVARIATE CALCULUS WHAT IS CALCULUS? 3:45:39 Welcome to Multivariate Calculus 3:47:29 Welcome to Module 1 3:48:33 Functions 3:52:51 Rise Over Run 3:57:48 Definition of a derivative 4:08:30 Differentiation example & special cases 4:16:19 Product rule 4:20:27 Chain rule 4:25:50 Taming a beast 4:31:29 See you next module! MULTIVARIATE CALCULUS 4:32:09 Welcome to Module2! 4:33:13 Variables, constants & context 4:41:09 Differentiate with respect to anything 4:45:53 The Jacobian 4:51:42 Jacobian applied 4:58:05 The Sandpit 5:02:48 The Hessian 5:08:27 Reality in hard 5:13:04 See you next module! MULTIVARIATE CHAIN RULE AND ITS APPLICATIONS 5:13:28 Welcome to Module 3! 5:14:04 Multivariate chain rule 5:16:43 More multivariate chain rule 5:22:21 Simple neural networks 5:28:13 More simple neural networks 5:32:25 See you next module! TAYLOR SERIES AND LINEARISATION 5:32:59 Welcome to Module! 5:33:35 Building approximate functions 5:37:03 Power Series 5:40:41 Power series derivation 5:49:50 Power series datails 5:56:04 Examples 6:01:24 Linearisation 6:06:41 Multivariate Taylor 6:13:08 See you next module! INTRO TO OPTIMISATION 6:13:36 Welcome to Module 5! 6:21:51 Gradient Descent 6:30:58 constrianed optimisation 6:39:32 See you next module! REGRESSION 6:41:40 simple linear regression 6:51:52 General non linear least squares 6:59:05 Doing least squares regression analysis in practice 7:05:24 Wrap up of this course ------------------------------------------------------- The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge. COURSE 3 Mathematics for Machine Learning: PCA STATISTICS OF DATASETS 7:06:12 Introduction to the Course 7:09:59 Welcome to module 1 7:10:41 Mean of a dataset 7:14:41 Variance of one-dimensional datasets 7:19:36 Variance of higher -dimensional datasets 7:24:52 Effect on the mean 7:29:38 Effect on the (co)variance 7:33:08 See you next module! INNER PRODUCTS 7:33:35 Welcome to module 2 7:35:24 Dot product 7:40:07 Inner product definition 7:45:09 Inner product length of vectors 7:52:17 Inner product distance between vectors 7:55:59 Inner product angles and orthogonality 8:01:41 Inner product of functions and random variables (optional) 8:09:03 Heading for the next module! ORTHOGONAL PROJECTIONS 8:09:38 Welcome to module 3 8:10:19 Projection onto ID subspaces 8:18:02 Example projection onto ID Subspaces 8:12:28 Projections onto higher-dimensional subspaces 8:30:01 Example projection onto a 2D subspaces 8:33:53 This was module 3! PRINCIPAL COMPONENT ANALYSIS 8:34:26 Welcome to module 4 8:35:35 Problem setting and PCA objective 8:43:20 Finding the coordinates of the projected data 8:48:49 Reformulation of the objective 8:59:15 Finding the basis vectors that span the principal subspace 9:06:55 Steps of PCA 9:11:02 PCA in high dimensions 9:16:51 Other interpretations of PCA (optional) 9:24:33 Summary of this module 9:25:16 This was the course on PCA

[@Rixnex]

Can you add it to description so it could be accessible

[@vawulencenews9428]

No differential equation? I thought Machine learning requires differential equation

[@metaverse413]

I really wish they add this to the description box

[@i_chandanpatel]

Atleast pin this comment

[@marktahu2932]

Really appreciate this as a refresher that was needed after 40 odd years. Thanks heaps for the straightforward approach and the clarity.

[@NoamGonen]

Awesome lecture, great refresher for long forgotten theory

[@omar-elgammal]

This is extremely useful ! thanks a lot it helps me a lot with my Msc.

[@karlodjo6040]

😭😭😭 Thank a lot guys. GOD BLESS YOU.

[@alishera4673]

this video is incredible. thank you all very much.

[@masoomladkaaproudvegan2876]

awesome professor thanks a lot

[@creatorofimages7925]

Thank you! :) I clicked solely because of the very honest title of this video. MATHEMATICS for Machine Learning. That's how you generate the right "expectation" of students for a certain lecture/topic.

[@joelausten]

yup the keyword machine learning makes me motivated, this video is legend anyways.

[@avgspaceloveronasabbatical]

I learned a lot from this, thank you so much!

[@joelausten]

what lesson do you take before this, I find this hard to understand.

[@MyLesson007]

Deep Learning Specialization kzbin.info/aero/PLtS8Ubq2bIlUOQoopGBa_F2mQvdk6QeBw

[@dilsydiltak0101]

Kindly also share machine learning course...

[@007myzorro]

AWSOME GENIAL Make the things SO comprehensive and so playfully.

[@koffiflaimoiye5276]

Thanks you very much.

[@kartiksinghvi9949]

Thanks for the lecture 😊

[@constantin2002]

Thanks for great explain. Help me alot.

[@rihanbouhaddouch5418]

Thank you so much, this is really helpful.

[@joelausten]

Do you have any suggestion to help me understand this math, i find it hard from the first 30 minutes, confusing.

[@vicentegabrielscalisi6182]

Muy bueno. Felicitaciones 🎈

[@medrouabhi5699]

thanks you for this course ,,,i find it very iteressed

[@LoicMat]

Thank you so much for the video! For anyone wondering, the image is mirrored: check out 1:25:40, his (actual) right hand is the left hand in the video (on the side of the wrist watch)

[@LoicMat]

Oh and it's also explained explicitly at 2:47:35 :)

[@zubair1411]

This channel is really a savior

[@WildOne777]

Thank you sir. 😊 (Your videos on KZbin and classes are great!)

[@MyLesson007]

Glad you like them!

[@firstname4337]

these are NOT his videos -- he stole them from coursera

[@ramkirpallodhi3126]

Great course

[@kathryncassidy1500]

Amazing

[@mdfarhadhussain]

This is the best 9 hours you would ever spent on linear algebra

[@robopsychology]

excellent presentation, except perhaps the last part.

[@moukailasadikou2554]

Good job. Thank you so much

[@joelausten]

How'd you understand the lesson? I find these lessons hard to understand, do you any suggestion.

[@arslanjutt4282]

Sir please give one on statistics like this towards data science not as statistician

[@harshnaik6989]

Thanks a LOTTTTTTTTT🙏🙏🙏🙏🙏🙏

[@arpita1shrivas]

im in 10th grade, thank you so much for making this, i took notes for the entire 9 hour lecture and finished today.

[@MuhammadIbrahim-ju1tp]

Can you share the notes ?

[@sida_g567]

Cool

[@subramanianchenniappan4059]

Timestamps relieves headaches😅😅

[@glennisholcomb592]

i love the math,

[@BonesFrielinghaus]

Guys.... timestamps essential. Come onnn!

[@t.gossmann8731]

@7:24:47 in the bottom right of the screen the var(D) is calculated. If I hear is correctly, the speaker mentions it as being the covariance matrix. Is this correct? Without a 2nd index it can only be the variance like also written on the screen.

[@WithinEpsilon]

Why is the third course exclusive to this compilation. I don't see it on the Imperial College London channel.

[@007myzorro]

AWESOME PROFESSOR 🎉🎉🎉

[@karthikm627]

Please add timelines of topics 😊

[@lelouchlamperouge9220]

Pls add timestamps

[@labhambaheti]

Under rated comment

[@patheticweeb_6923]

There is time stamp in comments

[@marcosantonio7065]

up

[@ermuhambetcalmenov8104]

Thnx u

[@chrissemenov8901]

02:25:00

[@mabd10]

first lesson - 1:02:35 secod - 1:44:50

[@forheuristiclifeksh7836]

5:15:37

[@chessmaster856]

Machines learn. Why are we learning? These are simple programs which try to change model over time based on data or feedback

[@Sarkkoth]

To learn about the machines?

[@amritwt]

holy shit what a course

[@alexe3332]

Seriously frustrating to see no application

[@noah3528]

02:34:33

[@mahender2517]

Course's material please, thank you

[@MetaPhysStore0770]

Frog emerge from Tª-d/d+P⁰L=E

[@BR-hi6yt]

Suddenly changes vector meaning from House [20 (cost), 40 (area), 45(heating)] to spatial r, s etc. Where is i and j for the house example? So the price or heating has two orthogonal components? He skips over that point cleverly and sticks to high school known routes of spatial vectors where i and j are x and y - obviously. Its not obvious for the price, heating. But he avoids that or says "its the same thing". Teh later r1s + r2s = r.s - lol, he's mad.

[@Cat_Sterling]

Which specialization is being addressed in the video? Is it a specialization on EdX or Coursera?

[@kevinmcfarlane2752]

I don’t know about EdX but I recently completed this specialization (free track) on Coursera. Next up is Machine Learning Specialization. But I’m taking a diversion into some Generative AI courses.

[@Cat_Sterling]

@@kevinmcfarlane2752 do you remember the name of this specialization which you completed on Coursera?

[@svdfxd]

@@kevinmcfarlane2752 Do you have any suggestions for Generative AI course ?

[@ppanda8427]

How did he wrote backwards through whole video!

[@Shreya...1]

So basically 11th and 12th maths is required.

[@S.Carton_Esq.]

A 9+ hour video needs a concept/lesson index in the run-time clock. Put one in, and I might consider watching.

[@Turtlenigma]

he put time stamps in the comments

[@pectenmaximus231]

What an honour is your consideration

[@elemayelemay4229]

the car looks like alien's spaceship lmao

[@brospore7897]

Is he left handed and the image is mirrored? Or is he right handed and able to write on glass in reverse?

[@LoicMat]

The image is mirrored: check out 1:25:40, he's using his right hand, which is the one with the watch

[@TheGladiator123]

Does anyone know such a course like that for statistics

[@matattz]

kzbin.info/www/bejne/qJ6chIyOabJ3q5I&ab_channel=CarlosFernandez-Granda Carlos teaches statistics for Data Science and for me his way of teaching just works.

[@kevinmcfarlane2752]

I've just done one on Coursera. Probability and Statistics. It’s also part 3 of their Math for Machine Learning Specialization.

[@mawkuri5496]

dont tell me he was nancy pi when he was younger

[@KylianMbappe07303]

13:14 could anyone explain what are we trying to understand from here

[@joelausten]

how im confused till the 20 minutes

[@warisulimam3440]

Where can I find the exercises they mention throughout the lectures?

[@alokshandilya104]

on coursera

[@joelausten]

@@alokshandilya104 needs payment/

[@joelausten]

I find this lesson so confusing, do you have any recommendations on what to learn first.

[@tarshsingh4198]

8:09:12

[@PANDURANG99]

where is python code?

[@rohanrana7067]

can anyone tell me what should i learn in maths for coding? Iskill am working on statistics and probability.. do you need to know algebra, trigonometry, etc? As for simple interests and many more, we can just use the formula from chatgpt or Google.. I am new here in coding.. I am in my 2nd year of BA.. can someone tell me if I need to have a Btech or IT background or just skill and certificate matters? i am doing certificate course in web dev and dsa

[@sugarmy9683]

you dont need any math for web dev just high school level maths is more then enough

[@rohanrana7067]

@@sugarmy9683 my question was for coding in advance level, like cybersecurity, ml, ai, deep learning, clouding etc

[@kevinchristopher5180]

@@rohanrana7067 for ml,dl or some data analytics means this video much for you

[@master_braure]

15:27

[@master_braure]

38:28

[@master_braure]

51:07

[@CyberSec-zx6oy]

Already lost on the start

[@joelausten]

howww i want to understand but it doesnt even from the beginning

[@pesgamer00]

Is this video enough to learn machine learning? Anyone please give a reply 😢

[@Yesterday_i_ate_rat]

Yes

[@joelausten]

@@Yesterday_i_ate_rat do you understand the lesson that i taught in this video? I find this hard to understand. Do you have any recommendations.

[@Yesterday_i_ate_rat]

@@joelausten first start by the new video from @freecodecamp "linear algebra for ml, dl, gen ai" and solve easy to medium questions to get a good understanding of topics and build confidence Don't try to grasp all these in one go,,, give this linear algebra a good amount of time, divide all the topics in different sections and complete it in 1-2 months Then pick the "statistics for ds" from @datatab ( yt - both inferential and descriptive ) and understand the topics After that pick calculus , for calculus I didn't find any good yt video, that's why, I will suggest you to learn from books which has good amount of questions

[@alexzhang9318]

Your 'b' looks like 6

[@vickey27able]

Jo Bharat ko pahle se kaafi jyada economically, defence, international stage pe top jo bhi kar sakta he, chahe BJP or Congress, isme vote mangne ke lie koi sharm ki baat nahi, hum public ko hamara Bharat top 5 me chahie, so asking for vote is not a sin for any great son or daughter of India who is keep working day n night to make India develop 🇮🇳

[@frafranildo]

I don't like that you spent so much time selling me why I should want to learn about vectors. Almost like I'm supposed to dislike it.

[@InfiniteWaveMusic]

Lol

[@vedmishravlogging]

------------ TIME STAMP ------------- In the first course on Linear Algebra we look at what linear algebra is and how it relates to data. Then we look through what vectors and matrices are and how to work with them. COURSE 1 MATHEMATICS FOR MACHINE LEARNING:LINEAR ALGEBRA INTRODUCTION TO LINEAR ALGEBRA AND TO MATHEMATICS FOR MACHINE LEARNING 0:00:00 Introduction Solving data science challenges with mathemaatics 0:02:27 Motivations for linear algebra 0:05:57 Getting a handle on vectors 0:15:03 Operations with vectors 0:26:32 Summary VECTORS ARE OBJECTS THAT MOVE AROUND SPACE 0:27:37 Introduction to module 2 - Vectors 0:28:27 Modulus & inner product 0:38:28 Cosine & dot product 0:44:21 Project 0:51:09 changing basis 1:02:34 Basis, Vector space, and linear independence 1:06:47 Application of changing basis 1:10:16 Summary MATRICES IN LINEAR ALGEBRA:OBJECTS THAT OPERATE ON VECTORS 1:11:36 Matrices, Vectors, and solving simultaneous equation problems 1:17:08 How matrices transform space 1:22:49 Types of matrix transformation 1:31:28 Composition or combination of matrix transformations 1:40:28 Solving the apples and bananas problem Gaussian elimination 1:48:29 Going from Gaussian elimination to finding the inverse matrix 1:57:07 Determinants and inverses 2:07:44 Summary MATRICES MAKE LINEAR MAPPINGS 2:08:43 Introduction Eintein summation convention and the symmetry of the dot product 2:18:37 Matrices changing basis 2:29:52 Doing a transformation in a changed basis 2:34:30 Orthogonal matrices 2:41:10 The Gram-Schmidt process 2:47:18 Example Reflecting in a plane EIGENVALUES AND EIGENVECTORS:APPLICATION TO DATA PROBLEMS 3:01:28 Welcome to Module 5 3:02:20 What are eigenvalues and eigenvectors 3:06:45 Special eigen-cases 3:10:17 Calculating eigenvectors 3:20:25 Changing to the eigenbasis 3:26:17 Eigenbasis example 3:33:43 Introduction to PageRank 3:42:27 Summary 3:43:42 Wrap up of this linear algebra course ---------------------------------------------- The second course, Multivariate Calculus, builds on this to look at how to optimize fitting functions to get good fits to data. It starts from introductory calculus and then uses the matrices and vectors from the first course to look at data fitting. Course 2 MULTIVARIATE CALCULUS WHAT IS CALCULUS? 3:45:39 Welcome to Multivariate Calculus 3:47:29 Welcome to Module 1 3:48:33 Functions 3:52:51 Rise Over Run 3:57:48 Definition of a derivative 4:08:30 Differentiation example & special cases 4:16:19 Product rule 4:20:27 Chain rule 4:25:50 Taming a beast 4:31:29 See you next module! MULTIVARIATE CALCULUS 4:32:09 Welcome to Module2! 4:33:13 Variables, constants & context 4:41:09 Differentiate with respect to anything 4:45:53 The Jacobian 4:51:42 Jacobian applied 4:58:05 The Sandpit 5:02:48 The Hessian 5:08:27 Reality in hard 5:13:04 See you next module! MULTIVARIATE CHAIN RULE AND ITS APPLICATIONS 5:13:28 Welcome to Module 3! 5:14:04 Multivariate chain rule 5:16:43 More multivariate chain rule 5:22:21 Simple neural networks 5:28:13 More simple neural networks 5:32:25 See you next module! TAYLOR SERIES AND LINEARISATION 5:32:59 Welcome to Module! 5:33:35 Building approximate functions 5:37:03 Power Series 5:40:41 Power series derivation 5:49:50 Power series datails 5:56:04 Examples 6:01:24 Linearisation 6:06:41 Multivariate Taylor 6:13:08 See you next module! INTRO TO OPTIMISATION 6:13:36 Welcome to Module 5! 6:21:51 Gradient Descent 6:30:58 constrianed optimisation 6:39:32 See you next module! REGRESSION 6:41:40 simple linear regression 6:51:52 General non linear least squares 6:59:05 Doing least squares regression analysis in practice 7:05:24 Wrap up of this course ------------------------------------------------------- The third course, Dimensionality Reduction with Principal Component Analysis, uses the mathematics from the first two courses to compress high-dimensional data. This course is of intermediate difficulty and will require Python and numpy knowledge. COURSE 3 Mathematics for Machine Learning: PCA STATISTICS OF DATASETS 7:06:12 Introduction to the Course 7:09:59 Welcome to module 1 7:10:41 Mean of a dataset 7:14:41 Variance of one-dimensional datasets 7:19:36 Variance of higher -dimensional datasets 7:24:52 Effect on the mean 7:29:38 Effect on the (co)variance 7:33:08 See you next module! INNER PRODUCTS 7:33:35 Welcome to module 2 7:35:24 Dot product 7:40:07 Inner product definition 7:45:09 Inner product length of vectors 7:52:17 Inner product distance between vectors 7:55:59 Inner product angles and orthogonality 8:01:41 Inner product of functions and random variables (optional) 8:09:03 Heading for the next module! ORTHOGONAL PROJECTIONS 8:09:38 Welcome to module 3 8:10:19 Projection onto ID subspaces 8:18:02 Example projection onto ID Subspaces 8:12:28 Projections onto higher-dimensional subspaces 8:30:01 Example projection onto a 2D subspaces 8:33:53 This was module 3! PRINCIPAL COMPONENT ANALYSIS 8:34:26 Welcome to module 4 8:35:35 Problem setting and PCA objective 8:43:20 Finding the coordinates of the projected data 8:48:49 Reformulation of the objective 8:59:15 Finding the basis vectors that span the principal subspace 9:06:55 Steps of PCA 9:11:02 PCA in high dimensions 9:16:51 Other interpretations of PCA (optional) 9:24:33 Summary of this module 9:25:16 This was the course on PCA

[@egosumcamax]

Up !

[@aibui3087]

you're so cool