Mathematical Foundations of Machine Learning

16h 25m 26s
English
Paid

Course description

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.

Read more about the course

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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#1: What Linear Algebra Is

All Course Lessons (112)

#Lesson TitleDurationAccess
1
What Linear Algebra Is Demo
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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