Mathematical Foundations of Machine Learning

16h 25m 26s
English
Paid
September 4, 2024

Mathematics forms the core of data science and machine learning. Thus, to be the best data scientist you can be, you must have a working understanding of the most relevant math. Getting started in data science is easy thanks to high-level libraries like Scikit-learn and Keras. But understanding the math behind the algorithms in these libraries opens an infinite number of possibilities up to you.

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From identifying modeling issues to inventing new and more powerful solutions, understanding the math behind it all can dramatically increase the impact you can make over the course of your career.

Led by deep learning guru Dr. Jon Krohn, this course provides a firm grasp of the mathematics — namely linear algebra and calculus — that underlies machine learning algorithms and data science models.

Course Sections

  1. Linear Algebra Data Structures

  2. Tensor Operations

  3. Matrix Properties

  4. Eigenvectors and Eigenvalues

  5. Matrix Operations for Machine Learning

  6. Limits

  7. Derivatives and Differentiation

  8. Automatic Differentiation

  9. Partial-Derivative Calculus

  10. Integral Calculus

Throughout each of the sections, you'll find plenty of hands-on assignments, Python code demos, and practical exercises to get your math game in top form!

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# Title Duration
1 What Linear Algebra Is 23:30
2 Plotting a System of Linear Equations 09:19
3 Linear Algebra Exercise 05:07
4 Tensors 02:34
5 Scalars 13:05
6 Vectors and Vector Transposition 12:20
7 Norms and Unit Vectors 14:38
8 Basis, Orthogonal, and Orthonormal Vectors 04:31
9 Matrix Tensors 08:24
10 Generic Tensor Notation 06:44
11 Exercises on Algebra Data Structures 02:08
12 Segment Intro 01:20
13 Tensor Transposition 03:53
14 Basic Tensor Arithmetic, incl. the Hadamard Product 06:13
15 Tensor Reduction 03:32
16 The Dot Product 05:14
17 Exercises on Tensor Operations 02:39
18 Solving Linear Systems with Substitution 09:48
19 Solving Linear Systems with Elimination 11:48
20 Visualizing Linear Systems 11:00
21 Segment Intro 02:06
22 The Frobenius Norm 05:02
23 Matrix Multiplication 24:29
24 Symmetric and Identity Matrices 04:42
25 Matrix Multiplication Exercises 07:22
26 Matrix Inversion 17:07
27 Diagonal Matrices 03:26
28 Orthogonal Matrices 05:17
29 Orthogonal Matrix Exercises 15:00
30 Segment Intro 17:53
31 Applying Matrices 07:32
32 Affine Transformations 18:21
33 Eigenvectors and Eigenvalues 26:14
34 Matrix Determinants 08:05
35 Determinants of Larger Matrices 08:42
36 Determinant Exercises 04:42
37 Determinants and Eigenvalues 15:44
38 Eigendecomposition 12:16
39 Eigenvector and Eigenvalue Applications 12:30
40 Segment Intro 03:22
41 Singular Value Decomposition 10:50
42 Data Compression with SVD 11:00
43 The Moore-Penrose Pseudoinverse 12:24
44 Regression with the Pseudoinverse 18:25
45 The Trace Operator 04:37
46 Principal Component Analysis (PCA) 08:28
47 Resources for Further Study of Linear Algebra 05:38
48 Segment Intro 03:40
49 Intro to Differential Calculus 13:26
50 Intro to Integral Calculus 02:25
51 The Method of Exhaustion 06:46
52 Calculus of the Infinitesimals 09:34
53 Calculus Applications 08:36
54 Calculating Limits 17:50
55 Exercises on Limits 06:07
56 Segment Intro 01:17
57 The Delta Method 15:47
58 How Derivatives Arise from Limits 13:53
59 Derivative Notation 04:20
60 The Derivative of a Constant 01:30
61 The Power Rule 01:17
62 The Constant Multiple Rule 03:11
63 The Sum Rule 02:27
64 Exercises on Derivative Rules 11:09
65 The Product Rule 03:51
66 The Quotient Rule 04:05
67 The Chain Rule 06:46
68 Advanced Exercises on Derivative Rules 11:49
69 The Power Rule on a Function Chain 04:38
70 Segment Intro 01:50
71 What Automatic Differentiation Is 04:43
72 Autodiff with PyTorch 06:18
73 Autodiff with TensorFlow 03:53
74 The Line Equation as a Tensor Graph 19:42
75 Machine Learning with Autodiff 40:12
76 Segment Intro 22:39
77 What Partial Derivatives Are 29:23
78 Partial Derivative Exercises 06:16
79 Calculating Partial Derivatives with Autodiff 05:19
80 Advanced Partial Derivatives 14:40
81 Advanced Partial-Derivative Exercises 06:12
82 Partial Derivative Notation 02:28
83 The Chain Rule for Partial Derivatives 09:18
84 Exercises on the Multivariate Chain Rule 05:19
85 Point-by-Point Regression 15:25
86 The Gradient of Quadratic Cost 15:17
87 Descending the Gradient of Cost 12:53
88 The Gradient of Mean Squared Error 24:22
89 Backpropagation 06:00
90 Higher-Order Partial Derivatives 11:54
91 Exercise on Higher-Order Partial Derivatives 02:56
92 Segment Intro 02:45
93 Binary Classification 09:14
94 The Confusion Matrix 02:30
95 The Receiver-Operating Characteristic (ROC) Curve 09:43
96 What Integral Calculus Is 06:15
97 The Integral Calculus Rules 05:38
98 Indefinite Integral Exercises 02:59
99 Definite Integrals 06:48
100 Numeric Integration with Python 04:52
101 Definite Integral Exercise 04:25
102 Finding the Area Under the ROC Curve 03:36
103 Resources for the Further Study of Calculus 04:02
104 Congratulations! 01:56
105 Probability & Information Theory 07:40
106 A Brief History of Probability Theory 03:37
107 What Probability Theory Is 05:16
108 Events and Sample Spaces 08:36
109 Multiple Independent Observations 08:03
110 Combinatorics 06:48
111 Exercises on Event Probabilities 09:57
112 More Lectures are on their Way! 00:22

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