Mathematical Foundations of Machine Learning

Mathematical Foundations of Machine Learning

English | MP4 | AVC 1280×720 | AAC 44KHz 2ch | 15.5 Hours | 4.30 GB

Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch

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. From identifying modeling issues to inventing new and more powerful solutions, understanding the math behind it all can dramatically increasing 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 the linear algebra and calculus — that underlies machine learning algorithms and data science models.

Course Sections

  • Linear Algebra Data Structures
  • Tensor Operations
  • Matrix Properties
  • Eigenvectors and Eigenvalues
  • Matrix Operations for Machine Learning
  • Limits
  • Derivatives and Differentiation
  • Automatic Differentiation
  • Partial-Derivative Calculus
  • 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!

What you’ll learn

  • Understand the fundamentals of linear algebra and calculus, critical mathematical subjects underlying all of machine learning and data science
  • Manipulate tensors using all three of the most important Python tensor libraries: NumPy, TensorFlow, and PyTorch
  • How to apply all of the essential vector and matrix operations for machine learning and data science
  • Reduce the dimensionality of complex data to the most informative elements with eigenvectors, SVD, and PCA
  • Solve for unknowns with both simple techniques (e.g., elimination) and advanced techniques (e.g., pseudoinversion)
  • Appreciate how calculus works, from first principles, via interactive code demos in Python
  • Intimately understand advanced differentiation rules like the chain rule
  • Compute the partial derivatives of machine-learning cost functions by hand as well as with TensorFlow and PyTorch
  • Grasp exactly what gradients are and appreciate why they are essential for enabling ML via gradient descent
  • Use integral calculus to determine the area under any given curve
  • Be able to more intimately grasp the details of cutting-edge machine learning papers
  • Develop an understanding of what’s going on beneath the hood of machine learning algorithms, including those used for deep learning
Table of Contents

Data Structures for Linear Algebra
1 Introduction
2 What Linear Algebra Is
3 Plotting a System of Linear Equations
4 Linear Algebra Exercise
5 Tensors
6 Scalars
7 Vectors and Vector Transposition
8 Norms and Unit Vectors
9 Basis, Orthogonal, and Orthonormal Vectors
10 Matrix Tensors
11 Generic Tensor Notation
12 Exercises on Algebra Data Structures

Tensor Operations
13 Segment Intro
14 Tensor Transposition
15 Basic Tensor Arithmetic, incl. the Hadamard Product
16 Tensor Reduction
17 The Dot Product
18 Exercises on Tensor Operations
19 Solving Linear Systems with Substitution
20 Solving Linear Systems with Elimination
21 Visualizing Linear Systems

Matrix Properties
22 Segment Intro
23 The Frobenius Norm
24 Matrix Multiplication
25 Symmetric and Identity Matrices
26 Matrix Multiplication Exercises
27 Matrix Inversion
28 Diagonal Matrices
29 Orthogonal Matrices
30 Orthogonal Matrix Exercises

Eigenvectors and Eigenvalues
31 Segment Intro
32 Applying Matrices
33 Affine Transformations
34 Eigenvectors and Eigenvalues
35 Matrix Determinants
36 Determinants of Larger Matrices
37 Determinant Exercises
38 Determinants and Eigenvalues
39 Eigendecomposition
40 Eigenvector and Eigenvalue Applications

Matrix Operations for Machine Learning
41 Segment Intro
42 Singular Value Decomposition
43 Data Compression with SVD
44 The Moore-Penrose Pseudoinverse
45 Regression with the Pseudoinverse
46 The Trace Operator
47 Principal Component Analysis (PCA)
48 Resources for Further Study of Linear Algebra

Limits
49 Segment Intro
50 Intro to Differential Calculus
51 Intro to Integral Calculus
52 The Method of Exhaustion
53 Calculus of the Infinitesimals
54 Calculus Applications
55 Calculating Limits
56 Exercises on Limits

Derivatives and Differentiation
57 Segment Intro
58 The Delta Method
59 How Derivatives Arise from Limits
60 Derivative Notation
61 The Derivative of a Constant
62 The Power Rule
63 The Constant Multiple Rule
64 The Sum Rule
65 Exercises on Derivative Rules
66 The Product Rule
67 The Quotient Rule
68 The Chain Rule
69 Advanced Exercises on Derivative Rules
70 The Power Rule on a Function Chain

Automatic Differentiation
71 Segment Intro
72 What Automatic Differentiation Is
73 Autodiff with PyTorch
74 Autodiff with TensorFlow
75 The Line Equation as a Tensor Graph
76 Machine Learning with Autodiff

Partial Derivative Calculus
77 Segment Intro
78 What Partial Derivatives Are
79 Partial Derivative Exercises
80 Calculating Partial Derivatives with Autodiff
81 Advanced Partial Derivatives
82 Advanced Partial-Derivative Exercises
83 Partial Derivative Notation
84 The Chain Rule for Partial Derivatives
85 Exercises on the Multivariate Chain Rule
86 Point-by-Point Regression
87 The Gradient of Quadratic Cost
88 Descending the Gradient of Cost
89 The Gradient of Mean Squared Error
90 Backpropagation
91 Higher-Order Partial Derivatives
92 Exercise on Higher-Order Partial Derivatives

Integral Calculus
93 Segment Intro
94 Binary Classification
95 The Confusion Matrix
96 The Receiver-Operating Characteristic (ROC) Curve
97 What Integral Calculus Is
98 The Integral Calculus Rules
99 Indefinite Integral Exercises
100 Definite Integrals
101 Numeric Integration with Python
102 Definite Integral Exercise
103 Finding the Area Under the ROC Curve
104 Resources for the Further Study of Calculus
105 More Lectures are on their Way

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