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

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My Lesson

My Lesson

2 жыл бұрын

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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Пікірлер: 112
@MyLesson007
@MyLesson007 2 жыл бұрын
------------ 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
@Rixnex 2 жыл бұрын
Can you add it to description so it could be accessible
@vawulencenews9428
@vawulencenews9428 9 ай бұрын
No differential equation? I thought Machine learning requires differential equation
@metaverse413
@metaverse413 9 ай бұрын
I really wish they add this to the description box
@i_chandanpatel
@i_chandanpatel 5 ай бұрын
Atleast pin this comment
@marktahu2932
@marktahu2932 6 ай бұрын
Really appreciate this as a refresher that was needed after 40 odd years. Thanks heaps for the straightforward approach and the clarity.
@NoamGonen
@NoamGonen 6 ай бұрын
Awesome lecture, great refresher for long forgotten theory
@omar-elgammal
@omar-elgammal 8 ай бұрын
This is extremely useful ! thanks a lot it helps me a lot with my Msc.
@karlodjo6040
@karlodjo6040 2 жыл бұрын
😭😭😭 Thank a lot guys. GOD BLESS YOU.
@alishera4673
@alishera4673 6 ай бұрын
this video is incredible. thank you all very much.
@masoomladkaaproudvegan2876
@masoomladkaaproudvegan2876 2 жыл бұрын
awesome professor thanks a lot
@creatorofimages7925
@creatorofimages7925 6 ай бұрын
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
@joelausten Ай бұрын
yup the keyword machine learning makes me motivated, this video is legend anyways.
@avgspaceloveronasabbatical
@avgspaceloveronasabbatical 6 ай бұрын
I learned a lot from this, thank you so much!
@joelausten
@joelausten 26 күн бұрын
what lesson do you take before this, I find this hard to understand.
@MyLesson007
@MyLesson007 2 жыл бұрын
Deep Learning Specialization kzbin.info/aero/PLtS8Ubq2bIlUOQoopGBa_F2mQvdk6QeBw
@dilsydiltak0101
@dilsydiltak0101 Жыл бұрын
Kindly also share machine learning course...
@007myzorro
@007myzorro 4 ай бұрын
AWSOME GENIAL Make the things SO comprehensive and so playfully.
@koffiflaimoiye5276
@koffiflaimoiye5276 7 ай бұрын
Thanks you very much.
@kartiksinghvi9949
@kartiksinghvi9949 2 жыл бұрын
Thanks for the lecture 😊
@constantin2002
@constantin2002 6 күн бұрын
Thanks for great explain. Help me alot.
@rihanbouhaddouch5418
@rihanbouhaddouch5418 11 ай бұрын
Thank you so much, this is really helpful.
@joelausten
@joelausten 26 күн бұрын
Do you have any suggestion to help me understand this math, i find it hard from the first 30 minutes, confusing.
@vicentegabrielscalisi6182
@vicentegabrielscalisi6182 5 ай бұрын
Muy bueno. Felicitaciones 🎈
@medrouabhi5699
@medrouabhi5699 5 ай бұрын
thanks you for this course ,,,i find it very iteressed
@LoicMat
@LoicMat 5 ай бұрын
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
@LoicMat 5 ай бұрын
Oh and it's also explained explicitly at 2:47:35 :)
@zubair1411
@zubair1411 2 жыл бұрын
This channel is really a savior
@WildOne777
@WildOne777 2 жыл бұрын
Thank you sir. 😊 (Your videos on KZbin and classes are great!)
@MyLesson007
@MyLesson007 2 жыл бұрын
Glad you like them!
@firstname4337
@firstname4337 5 ай бұрын
these are NOT his videos -- he stole them from coursera
@ramkirpallodhi3126
@ramkirpallodhi3126 5 ай бұрын
Great course
@kathryncassidy1500
@kathryncassidy1500 Жыл бұрын
Amazing
@mdfarhadhussain
@mdfarhadhussain 6 ай бұрын
This is the best 9 hours you would ever spent on linear algebra
@robopsychology
@robopsychology 5 ай бұрын
excellent presentation, except perhaps the last part.
@moukailasadikou2554
@moukailasadikou2554 4 ай бұрын
Good job. Thank you so much
@joelausten
@joelausten 26 күн бұрын
How'd you understand the lesson? I find these lessons hard to understand, do you any suggestion.
@arslanjutt4282
@arslanjutt4282 6 ай бұрын
Sir please give one on statistics like this towards data science not as statistician
@harshnaik6989
@harshnaik6989 Жыл бұрын
Thanks a LOTTTTTTTTT🙏🙏🙏🙏🙏🙏
@arpita1shrivas
@arpita1shrivas 4 ай бұрын
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
@MuhammadIbrahim-ju1tp 3 ай бұрын
Can you share the notes ?
@sida_g567
@sida_g567 2 жыл бұрын
Cool
@subramanianchenniappan4059
@subramanianchenniappan4059 6 ай бұрын
Timestamps relieves headaches😅😅
@glennisholcomb592
@glennisholcomb592 5 ай бұрын
i love the math,
@BonesFrielinghaus
@BonesFrielinghaus 2 ай бұрын
Guys.... timestamps essential. Come onnn!
@t.gossmann8731
@t.gossmann8731 5 ай бұрын
@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
@WithinEpsilon 10 ай бұрын
Why is the third course exclusive to this compilation. I don't see it on the Imperial College London channel.
@007myzorro
@007myzorro 6 ай бұрын
AWESOME PROFESSOR 🎉🎉🎉
@karthikm627
@karthikm627 5 ай бұрын
Please add timelines of topics 😊
@lelouchlamperouge9220
@lelouchlamperouge9220 Жыл бұрын
Pls add timestamps
@labhambaheti
@labhambaheti 6 ай бұрын
Under rated comment
@patheticweeb_6923
@patheticweeb_6923 6 ай бұрын
There is time stamp in comments
@marcosantonio7065
@marcosantonio7065 5 ай бұрын
up
@ermuhambetcalmenov8104
@ermuhambetcalmenov8104 4 ай бұрын
Thnx u
@chrissemenov8901
@chrissemenov8901 7 ай бұрын
02:25:00
@mabd10
@mabd10 Ай бұрын
first lesson - 1:02:35 secod - 1:44:50
@forheuristiclifeksh7836
@forheuristiclifeksh7836 5 ай бұрын
5:15:37
@chessmaster856
@chessmaster856 6 ай бұрын
Machines learn. Why are we learning? These are simple programs which try to change model over time based on data or feedback
@Sarkkoth
@Sarkkoth 6 ай бұрын
To learn about the machines?
@amritwt
@amritwt 7 ай бұрын
holy shit what a course
@alexe3332
@alexe3332 5 ай бұрын
Seriously frustrating to see no application
@noah3528
@noah3528 Ай бұрын
02:34:33
@mahender2517
@mahender2517 2 жыл бұрын
Course's material please, thank you
@MetaPhysStore0770
@MetaPhysStore0770 5 ай бұрын
Frog emerge from Tª-d/d+P⁰L=E
@BR-hi6yt
@BR-hi6yt 5 ай бұрын
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
@Cat_Sterling 6 ай бұрын
Which specialization is being addressed in the video? Is it a specialization on EdX or Coursera?
@kevinmcfarlane2752
@kevinmcfarlane2752 6 ай бұрын
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
@Cat_Sterling 6 ай бұрын
@@kevinmcfarlane2752 do you remember the name of this specialization which you completed on Coursera?
@svdfxd
@svdfxd 4 ай бұрын
@@kevinmcfarlane2752 Do you have any suggestions for Generative AI course ?
@ppanda8427
@ppanda8427 Ай бұрын
How did he wrote backwards through whole video!
@Shreya...1
@Shreya...1 4 ай бұрын
So basically 11th and 12th maths is required.
@S.Carton_Esq.
@S.Carton_Esq. 6 ай бұрын
A 9+ hour video needs a concept/lesson index in the run-time clock. Put one in, and I might consider watching.
@Turtlenigma
@Turtlenigma 6 ай бұрын
he put time stamps in the comments
@pectenmaximus231
@pectenmaximus231 2 ай бұрын
What an honour is your consideration
@elemayelemay4229
@elemayelemay4229 11 ай бұрын
the car looks like alien's spaceship lmao
@brospore7897
@brospore7897 6 ай бұрын
Is he left handed and the image is mirrored? Or is he right handed and able to write on glass in reverse?
@LoicMat
@LoicMat 5 ай бұрын
The image is mirrored: check out 1:25:40, he's using his right hand, which is the one with the watch
@TheGladiator123
@TheGladiator123 Жыл бұрын
Does anyone know such a course like that for statistics
@matattz
@matattz 7 ай бұрын
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
@kevinmcfarlane2752 6 ай бұрын
I've just done one on Coursera. Probability and Statistics. It’s also part 3 of their Math for Machine Learning Specialization.
@mawkuri5496
@mawkuri5496 3 күн бұрын
dont tell me he was nancy pi when he was younger
@KylianMbappe07303
@KylianMbappe07303 8 ай бұрын
13:14 could anyone explain what are we trying to understand from here
@joelausten
@joelausten 29 күн бұрын
how im confused till the 20 minutes
@warisulimam3440
@warisulimam3440 3 ай бұрын
Where can I find the exercises they mention throughout the lectures?
@alokshandilya104
@alokshandilya104 2 ай бұрын
on coursera
@joelausten
@joelausten 26 күн бұрын
@@alokshandilya104 needs payment/
@joelausten
@joelausten 26 күн бұрын
I find this lesson so confusing, do you have any recommendations on what to learn first.
@tarshsingh4198
@tarshsingh4198 Жыл бұрын
8:09:12
@PANDURANG99
@PANDURANG99 10 сағат бұрын
where is python code?
@rohanrana7067
@rohanrana7067 2 ай бұрын
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
@sugarmy9683 Ай бұрын
you dont need any math for web dev just high school level maths is more then enough
@rohanrana7067
@rohanrana7067 Ай бұрын
@@sugarmy9683 my question was for coding in advance level, like cybersecurity, ml, ai, deep learning, clouding etc
@kevinchristopher5180
@kevinchristopher5180 18 күн бұрын
@@rohanrana7067 for ml,dl or some data analytics means this video much for you
@master_braure
@master_braure 4 ай бұрын
15:27
@master_braure
@master_braure 4 ай бұрын
38:28
@master_braure
@master_braure 4 ай бұрын
51:07
@CyberSec-zx6oy
@CyberSec-zx6oy 5 ай бұрын
Already lost on the start
@joelausten
@joelausten 29 күн бұрын
howww i want to understand but it doesnt even from the beginning
@pesgamer00
@pesgamer00 2 ай бұрын
Is this video enough to learn machine learning? Anyone please give a reply 😢
@Yesterday_i_ate_rat
@Yesterday_i_ate_rat Ай бұрын
Yes
@joelausten
@joelausten 26 күн бұрын
@@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
@Yesterday_i_ate_rat 26 күн бұрын
@@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
@alexzhang9318 5 ай бұрын
Your 'b' looks like 6
@vickey27able
@vickey27able 6 ай бұрын
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
@frafranildo 4 ай бұрын
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
@InfiniteWaveMusic 6 ай бұрын
Lol
@vedmishravlogging
@vedmishravlogging 6 ай бұрын
------------ 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
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