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Mathematical Foundations of Machine Learning by Udemy
Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch
Course Highlights
- 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
Skills you will learn!
Curriculum
12 Topics
Introduction
What Linear Algebra Is
Plotting a System of Linear Equations
Linear Algebra Exercise
Tensors
Scalars
Vectors and Vector Transposition
Norms and Unit Vectors
Basis Orthogonal and Orthonormal Vectors
Matrix Tensors
Generic Tensor Notation
Exercises on Algebra Data Structures
9 Topics
Segment Intro
Tensor Transposition
Basic Tensor Arithmetic incl. the Hadamard Product
Tensor Reduction
The Dot Product
Exercises on Tensor Operations
Solving Linear Systems with Substitution
Solving Linear Systems with Elimination
Visualizing Linear Systems
9 Topics
Segment Intro
The Frobenius Norm
Matrix Multiplication
Symmetric and Identity Matrices
Matrix Multiplication Exercises
Matrix Inversion
Diagonal Matrices
Orthogonal Matrices
Orthogonal Matrix Exercises
10 Topics
Segment Intro
Applying Matrices
Affine Transformations
Eigenvectors and Eigenvalues
Matrix Determinants
Determinants of Larger Matrices
Determinant Exercises
Determinants and Eigenvalues
Eigendecomposition
Eigenvector and Eigenvalue Applications
8 Topics
Segment Intro
Singular Value Decomposition
Data Compression with SVD
The Moore-Penrose Pseudoinverse
Regression with the Pseudoinverse
The Trace Operator
Principal Component Analysis (PCA)
Resources for Further Study of Linear Algebra
8 Topics
Segment Intro
Intro to Differential Calculus
Intro to Integral Calculus
The Method of Exhaustion
Calculus of the Infinitesimals
Calculus Applications
Calculating Limits
Exercises on Limits
14 Topics
Segment Intro
The Delta Method
How Derivatives Arise from Limits
Derivative Notation
The Derivative of a Constant
The Power Rule
The Constant Multiple Rule
The Sum Rule
Exercises on Derivative Rules
The Product Rule
The Quotient Rule
The Chain Rule
Advanced Exercises on Derivative Rules
The Power Rule on a Function Chain
6 Topics
Segment Intro
What Automatic Differentiation Is
Autodiff with PyTorch
Autodiff with TensorFlow
The Line Equation as a Tensor Graph
Machine Learning with Autodiff
16 Topics
Segment Intro
What Partial Derivatives Are
Partial Derivative Exercises
Calculating Partial Derivatives with Autodiff
Advanced Partial Derivatives
Advanced Partial-Derivative Exercises
Partial Derivative Notation
The Chain Rule for Partial Derivatives
Exercises on the Multivariate Chain Rule
Point-by-Point Regression
The Gradient of Quadratic Cost
Descending the Gradient of Cost
The Gradient of Mean Squared Error
Backpropagation
Higher-Order Partial Derivatives
Exercise on Higher-Order Partial Derivatives
13 Topics
Segment Intro
Binary Classification
The Confusion Matrix
The Receiver-Operating Characteristic (ROC) Curve
What Integral Calculus Is
The Integral Calculus Rules
Indefinite Integral Exercises
Definite Integrals
Numeric Integration with Python
Definite Integral Exercise
Finding the Area Under the ROC Curve
Resources for the Further Study of Calculus
Congratulations!
8 Topics
Probability & Information Theory
A Brief History of Probability Theory
What Probability Theory Is
Events and Sample Spaces
Multiple Independent Observations
Combinatorics
Exercises on Event Probabilities
More Lectures are on their Way!
1 Topic
BONUS: Cloud Skills for ML & AI (COUPON inside)
Mathematical Foundations of Machine Learning
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