### Course Description

In this course, we cover core topics such as:
• Linear Regression
• Linear Discriminant Analysis
• Logistic Regression
• Artificial Neural Networks
• Support Vector Machines

#### What am I going to get from this course?

Refresh your machine learning knowledge.

Apply fundamental techniques of machine learning.

Gain a firm foundation in machine learning for furthering your career.

Learn a subject crucial for Data Science and Artificial Intelligence.

### Prerequisites and Target Audience

#### What will students need to know or do before starting this course?

Linear algebra, multivariable calculus, probability.

Any computational software. E.g. Mathematica.

#### Who should take this course? Who should not?

Anyone interested in gaining mastery of machine learning.

Data scientists.

AI professionals.

### Curriculum

#### Module 2: Linear Regression

Lecture 2
Linear Regression
Students will learn about the notion of residual sum of squares.

Lecture 3
The Least Squares Method
Students will learn how to apply the least squares method to solve the least squares problem.

Lecture 4
Linear Algebra Solution to Least Squares Problem
Students will learn about a linear algebra approach to solving the least squares problem.

Lecture 5
Example: Linear Regression
An example of applying the least squares method is provided.

Lecture 6
Summary: Linear Regression
A summary of linear regression is provided.

Lecture 7
Problem Set: Linear Regression
Practice Problems for Linear Regression are provided.

Lecture 8
Solution Set: Linear Regression
Solutions are provided for Problem Set: Linear Regression.

#### Module 3: Linear Discriminant Analysis

Students will be introduced to classification problems.

Lecture 10
Linear Discriminant Analysis
The method of linear discriminant analysis is introduced.

Lecture 11
The Posterior Probability Functions

In this lecture, we build a formula for the posterior probability.

Lecture 12
Modelling the Posterior Probability Functions

In this lecture, we model the posterior probability functions.

Lecture 13
Linear Discriminant Functions

Students will learn what linear discriminant functions are.

Lecture 14
Estimating the Linear Discriminant Functions

In this lecture, we estimate the linear discriminant functions.

Lecture 15
Classifying Data Points Using Linear Discriminant Functions

Students will learn how to classify data points using linear discriminant functions.

Students will see an example of applying linear discriminant analysis.

Another example of applying linear discriminant analysis is provided.

Lecture 18
Summary: Linear Discriminant Analysis

A summary of linear discriminant analysis is provided.

Lecture 19
Problem Set: Linear Discriminant Analysis

Practice problems for Linear Discriminant Analysis are provided.

Lecture 20
Solution Set: Linear Discriminant Analysis

Solutions are provided for Problem Set: Linear Discriminant Analysis.

#### Module 4: Logistic Regression

Lecture 21
Logistic Regression
The method of logistic regression is introduced.

Lecture 22
Logistic Regression Model of the Posterior Probability Function

In this lecture, we model the posterior probability function.

Lecture 23
Estimating the Posterior Probability Function

In this lecture, we introduce a strategy for estimating the posterior probability function.

Lecture 24
The Multivariate Newton-Raphson Method

Students will learn how the Multivariate Newton-Raphson method is used to maximize a function.

Lecture 25
Maximizing the Log-Likelihood Function

In this lecture, we apply the multivariate Newton-Raphson method to the log-likelihood function and learn about iterative reweighted least squares.

Lecture 26
Example: Logistic Regression

Students will learn how to apply logistic regression to solve a classification problem.

Lecture 27
Summary: Logistic Regression

A summary of logistic regression is provided.

Lecture 28
Problem Set: Logistic Regression

Practice problems for Logistic Regression are provided.

Lecture 29
Solution Set: Logistic Regression

Solutions are provided for Problem Set: Logistic Regression

#### Module 5: Artificial Neural Networks

Lecture 30
Artificial Neural Networks
An introduction to artificial neural networks is provided.

Lecture 31
Neural Network Model of the Output Functions
In this lecture, we build a neural network model for the output functions using a neural network diagram.

Lecture 32
Forward Propagation
The notion of forward propagation is discussed.

Lecture 33
Choosing Activation Functions
Students will learn which activation functions to choose for each type of problem.

Lecture 34
Estimating the Output Functions
We introduce a strategy for estimating the output functions.

Lecture 35
Error Function for Regression

Students will learn which error function to use for regression problems.

Lecture 36
Error Function for Binary Classification

Students will learn which error function to use for binary classification problems.

Lecture 37
Error Function for Multi-class Classification

Students will learn which error function to use for multi-class classification problems.

Lecture 38
Minimizing the Error Function Using Gradient Descent

Students will learn how gradient descent is used to minimize the error function.

Lecture 39
Backpropagation Equations

Students will learn how the backpropagation equations are used to help find the gradient of the error function.

Lecture 40
Summary of Backpropagation

A summary of backpropagation is provided.

Lecture 41
Summary: Artificial Neural Networks

A summary of artificial neural networks is provided.

Lecture 42
Problem Set: Artificial Neural Networks

Practice problems for Artificial Neural Networks are provided.

Lecture 43
Solution Set: Artificial Neural Networks

Solutions are provided for Problem Set: Artificial Neural Networks

#### Module 6: Maximal Margin Classifier

Lecture 44
Maximal Margin Classifier
An introduction to maximal margin classifier, support vector classifier, and support vector machine is provided.

Lecture 45
Definitions of Separating Hyperplane and Margin
In this lecture, we provide definitions of separating hyperplane and margin.

Lecture 46
Maximizing the Margin
in this lecture, we formulate a maximization problem.

Lecture 47
Definition of Maximal Margin Classifier
The maximal margin classifier is defined.

Lecture 48
Reformulating the Optimization Problem
In this lecture, we reformulate the maximization problem as a convex optimization problem.

Lecture 49
Solving the Convex Optimization Problem

We introduce a strategy for solving the optimization problem.

Lecture 50
KKT Conditions

Students will learn what the KKT conditions are.

Lecture 51
Primal and Dual Problems

Students will learn what the primal and dual problems are.

Lecture 52
Solving the Dual Problem

In this lecture, we solve the dual problem.

Lecture 53
The Coefficients for the Maximal Margin Hyperplane

Students will learn how to solve for the coefficients for the maximal margin hyperplane.

Lecture 54
The Support Vectors

We define what support vectors are.

Lecture 55
Classifying Test Points

Students will learn how to classify test points.

Lecture 56
Maximal Margin Classifier Example 1
An example of applying the maximal margin classifier to solve a classification problem is provided.

Lecture 57
Maximal Margin Classifier Example 2

A second example of applying the maximal margin classifier is provided.

Lecture 58
Summary: Maximal Margin Classifier

A summary of the maximal margin classifier is provided.

Lecture 59
Problem Set: Maximal Margin Classifier

Practice problems for Maximal Margin Classifier are provided.

Lecture 60
Solution Set: Maximal Margin Classifier

Solutions are provided for Problem Set: Maximal Margin Classifier

#### Module 7: Support Vector Classifier

Lecture 61
Support Vector Classifier
An introduction to the support vector classifier is provided.

Lecture 62
Slack Variables: Points on Correct Side of Hyperplane
We characterize points on the correct side of the hyperplane using slack variables.

Lecture 63
Slack Variables: Points on Wrong Side of Hyperplane
We characterize points on the wrong side of the hyperplane using slack variables.

Lecture 64
Formulating the Optimization Problem

We formulate the optimization problem for the support vector classifier.

Lecture 65
Definition of Support Vector Classifier

We define the support vector classifier.

Lecture 66
A Convex Optimization Problem

We identify the optimization problem as a convex optimization problem.

Lecture 67
Solving the Convex Optimization Problem (Soft Margin)

Students will learn how to solve the convex optimization problem using Lagrange multipliers.

Lecture 68
The Coefficients for the Soft Margin Hyperplane

Students will learn how to find the coefficients for the soft margin hyperplane.

Lecture 69
The Support Vectors (Soft Margin)

We define the support vectors for the support vector classifier.

Lecture 70
Classifying Test Points (Soft Margin)

Students will learn how to classify test points using the support vector classifier.

Lecture 71
Support Vector Classifier Example 1

Students will see how the support vector classifier works in a simple but specific example.

Lecture 72
Support Vector Classifier Example 2

Students will see how the support vector classifier works in a second simple but specific example.

Lecture 73
Summary: Support Vector Classifier

We review the support vector classifier.

Lecture 74
Problem Set: Support Vector Classifier

Practice problems for Support Vector Classifier are provided.

Lecture 75
Solution Set: Support Vector Classifier

Solutions are provided for Problem Set: Support Vector Classifier

#### Module 8: Support Vector Machine Classifier

Lecture 76
Support Vector Machine Classifier

An introduction to the support vector machine classifier is provided.

Lecture 77
Enlarging the Feature Space

Students will see how the support vector machine basically works.

Lecture 78
The Kernel Trick

Students will learn how the support vector machine classifier works by using the kernel trick.

Lecture 79
Summary: Support Vector Machine Classifier

We review the support vector machine classifier.

Lecture 80
Concluding Letter