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Mathematical Foundations of Machine Learning

Essential Linear Algebra and Calculus Hands-On in NumPy, TensorFlow, and PyTorch
Instructor:
Dr Jon Krohn
80,937 students enrolled
English [Auto]
Understand the fundamentals of linear algebra, a critical subject underlying all ML algorithms and data science models
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)
Be able to more intimately grasp the details of cutting-edge machine learning papers

To be a good data scientist, you need to know how to use data science and machine learning libraries and algorithms, such as Scikit-learn, TensorFlow, and PyTorch, to solve whatever problem you have at hand.

To be an excellent data scientist, you need to know how those libraries and algorithms work under the hood. This is where our Mathematical Foundations of Machine Learning comes in.

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.

The course is broken down into the following 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

We have finished filming additional content on calculus (Sections 8 through 10), which will be edited and uploaded by Summer 2021. At that point, the Mathematical Foundations of Machine Learning course could be considered complete, but we will continue adding related bonus content — on probability, statistics, data structures, and optimization — as quickly as we can. Enrollment now includes free, unlimited access to all of this future course content — over 25 hours in total.

Throughout each of the sections, you’ll find plenty of hands-on assignments, Python code demos, and practical exercises to get your math game up to speed!

Are you ready to become an outstanding data scientist? See you in the classroom.

Course Prerequisites

Programming: All code demos will be in Python so experience with it or another object-oriented programming language would be helpful for following along with the code examples.

Mathematics: Familiarity with secondary school-level mathematics will make the class easier to follow along with. If you are comfortable dealing with quantitative information — such as understanding charts and rearranging simple equations — then you should be well-prepared to follow along with all of the mathematics.

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

This is the first video in the course that makes heavy use of hands-on code demos. As described in the video, the default approach we assume for executing this code is within Jupyter notebooks within the (free!) Google Colab environment.

Pro tip: To prevent abuse of Colab (for, say, bitcoin mining), Colab sessions time out after a period of inactivity -- typically about 30 to 60 minutes. If your session times out, you'll lose all of the variables you had in memory, but you can quickly get back on track by following these three steps: 

  1. Click on the code cell you'd like to execute next.

  2. Select "Runtime" from the Colab menubar near the top of your screen.

  3. Select the "Run before" option. This executes all of the preceding cells and then you're good to go!

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

1
Segment Intro
2
Tensor Transposition
3
Basic Tensor Arithmetic, incl. the Hadamard Product
4
Tensor Reduction
5
The Dot Product
6
Exercises on Tensor Operations
7
Solving Linear Systems with Substitution
8
Solving Linear Systems with Elimination
9
Visualizing Linear Systems

Matrix Properties

1
Segment Intro
2
The Frobenius Norm
3
Matrix Multiplication
4
Symmetric and Identity Matrices
5
Matrix Multiplication Exercises
6
Matrix Inversion

While detailing how to determine the inverse of a matrix is outside the scope of this course, if you're keen to learn more on the topic, a clear tutorial can be found here: https://www.mathsisfun.com/algebra/matrix-inverse.html

7
Diagonal Matrices
8
Orthogonal Matrices
9
Orthogonal Matrix Exercises

Eigenvectors and Eigenvalues

1
Segment Intro
2
Applying Matrices
3
Affine Transformations
4
Eigenvectors and Eigenvalues
5
Matrix Determinants
6
Determinants of Larger Matrices
7
Determinant Exercises
8
Determinants and Eigenvalues
9
Eigendecomposition
10
Eigenvector and Eigenvalue Applications

Matrix Operations for Machine Learning

1
Segment Intro

Welcome to the final section of videos on linear algebra! In these videos, we cover the last key pieces of essential linear algebra you need to know to understand machine learning algorithms, including Singular Value Composition, Moore-Penrose Pseudoinversion, the Trace Operator, and Principal Component Analysis.

2
Singular Value Decomposition

With a focus on hands-on code demos in Python, in this video I introduce the theory and practice of singular value decomposition, a common linear algebra operation in the field of machine learning.

3
Data Compression with SVD

In this video, we take advantage of the singular value decomposition theory that we covered in the preceding video to dramatically compress data within a hands-on Python demo.

4
The Moore-Penrose Pseudoinverse

This video introduces Moore-Penrose pseudoinversion, a linear algebra concept that enables us to invert non-square matrices. The pseudoinverse is a critical machine learning concept because it solves for unknown variables within the non-square systems of equations that are common in machine learning. To show you how it works, we’ll use a hands-on code demo.

5
Regression with the Pseudoinverse

This is one of my favorite videos in the entire Machine Learning Foundations series! In it, we use Moore-Penrose pseudoinversion to solve for unknowns, enabling us to fit a line to points with linear algebra alone. When I first learned how to do this, it blew my mind -- I hope it blows your mind too!

6
The Trace Operator

This is a quick video on the Trace Operator, a relatively simple linear algebra concept, but one that frequently comes in handy for rearranging linear algebra equations, including ones that are common in machine learning.

7
Principal Component Analysis (PCA)

Via highly visual hands-on code demos in Python, this video introduces Principal Component Analysis, a prevalent and powerful machine learning technique for finding patterns in unlabeled data.

8
Resources for Further Study of Linear Algebra

Welcome to the final linear algebra video of my Machine Learning Foundations series! It’s a quick one to leave you with my favorite linear algebra resources so that you can dig deeper into the topics that pique your interest the most, if desired.

Limits

1
Segment Intro
2
Intro to Differential Calculus
3
Intro to Integral Calculus
4
The Method of Exhaustion
5
Calculus of the Infinitesimals
6
Calculus Applications
7
Calculating Limits
8
Exercises on Limits

Derivatives and Differentiation

1
Segment Intro
2
The Delta Method
3
How Derivatives Arise from Limits
4
Derivative Notation
5
The Derivative of a Constant
6
The Power Rule
7
The Constant Multiple Rule
8
The Sum Rule
9
Exercises on Derivative Rules
10
The Product Rule
11
The Quotient Rule
12
The Chain Rule
13
Advanced Exercises on Derivative Rules
14
The Power Rule on a Function Chain
15
More Lectures are on their Way!
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Mathematical Foundations of Machine Learning
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