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Complete Mathematical Intro to Machine Learning [2026]

Name: Complete Mathematical Intro to Machine Learning [2026]
Rating: 4.3 (7 reviews)

Taught by University Instructors | Learn the essentials of Machine Learning, including Theory, Coding, and Mathematics

Created byBlueGem Data Science

Last updated 1/2026

English

English [Auto],

What you'll learn

Master the fundamentals of Machine Learning, including Supervised & Unsupervised Learning
Use Python and R for Machine Learning Models
Learn Mathematical Foundations of the most common Machine Learning Frameworks
Learn to differentiate appropriate Machine Learning Models for specific use cases
Apply a refined toolbox of Algorithms for Data Science Problems
Understand how to fit Different Machine Learning Models for certain Applications
Experience Coding Examples to apply into other Projects
Experience hands-on Mathematical Examples of Models
Learn Neural Networks and Decision Trees
Understand k-Means Clustering and KNN Algorithms
Learn Support Vector Machines and Logistic Regression

Course content

16 sections • 110 lectures • 11h 15m total length

Outline2:31
This brief lecture provides an overview of the module and some prerequisites for the course.
Overview of Machine Learning7:35
This lecture provides a introduction to machine learning. We also differentiate some sister branches, namely AI and Data Science.
Supervised Learning Introduction11:06
This lecture introduces the formal supervised learning setup. We detail things like empirical risk minimization, loss, testing data, etc.
Why Test Data?1:57
This lecture outlines the need for test data as a means to approximate true risk. We also differentiate the difference between memorizing and true learning.
Unsupervised Machine Learning3:40
This lecture provides an overview of unsupervised learning. We also discuss some common use-cases and the formalized setup of UL.
Other Types of Learning1:33
This lecture briefly covers other types of learning such as Reinforcement Learning.
Supervised Learning Example: Mushroom Dataset15:54
This is an example of supervised learning done on the mushroom dataset. We encounter many common themes that come up in machine learning.
Machine Learning Issues: Bad Data4:05
In this lecture, we discuss a common issue engineers run into: bad data. We explore how bad data can yield limitations.
Machine Learning Issues: Under-Over fitting10:25
This lecture provides a brief overview of the bias-variance tradeoff. In particular, we discuss underfitting and overfitting -- common issues ML engineers encounter.
Intro to Machine Learning Formalism0:38
This lecture introduces the formalism to come in understanding machine learning.
Model Evaluation9:31
In this lecture, we discuss ways to assess model performance. We go further into empirical risk minimization and the importance of test data.
Machine Learning Trade-Offs6:41
In this lecture, we discuss trade-offs observed in machine learning. In particular, we mathematically work with the bias-variance trade-off.
Estimating the Regression Function5:21
This lecture outlines the foundations of regression function estimation and some nuance in the process.
More Complex Regression Functions3:20
In this lecture, we provide a brief example on regression, exploring rigid and flexible models.
The Bias-Variance Trade-Off3:26
This lecture details takeaways from the bias-variance trade-off and how engineers can use it to inform model evaluation.

Outline3:08
This video provides an introduction to the regression module and discusses the prerequisites required.
Intro and Motivating Example3:54
In this lecture, we provide an introduction to the objective of regression, outlining a motivating example.
Intro to Simple Linear Regression17:21
In this video, we mathematically and intuitively derive the foundations of OLS regression. We outline how the model is set up, the assumptions, and the method of estimation for a simple linear regression model.
With Intercept Model3:07
This lecture derives the estimators for with-intercept uni-variate regression models.
Example: Gentoo Penguins15:04
In this example, we fit with-intercept and without-intercept regression models to the Gentoo penguins dataset.
Derivation: Multiple Linear Regression7:20
In this lecture, we mathematically derive the beta-estimators in the multiple linear regression framework.
Example: Gapminder6:20
In this lecture, we solve the motivating example on the Gapminder dataset through R's functionality and directly.
Interpretation of OLS Output12:27
In this lecture, we explain the output of OLS and how it can be interpreted.
Hypothesis Testing7:56
In this lecture, we outline how to test the statistical significance of predictors by using hypothesis testing.
Confidence Intervals3:23
In this lecture, we discuss confidence intervals pertaining to regression estimators and model significance.
Model Evaluation3:45
In this lecture, we outline how to evaluate the performance of a regression model.
Feature Selection6:14
In this lecture, we outline methods of feature selection, including common step-wise algorithms.
Other Questions2:35
In this lecture, we outline some common paradigms and issues that we can encounter with regression and some possible ways to mitigate them.

Intro to Regularization3:05
In this lecture, we introduce regularization methods.
Ridge Regression4:33
In this lecture, we outline ridge regression and the benefits it can offer.
Best Subset Selection1:13
In this lecture, we discuss best subset discussion. We talk about the modified penalty term.
LASSO Regularization1:21
In this lecture, we modify the penalty term differently (by using the 1-norm) to yield LASSO regression.
Other Regression Variants2:28
In this lecture, we discuss alternative variants of regression.
Example: Gapminder Regularized Regression4:12
In this lecture, we work through an example on Gapminder data using regularization.

Non-Linear Modelling and Basis Functions5:38
In this lecture, we introduce and outline non-linear modelling and the use of basis functions.
Example: Polynomial Gapminder3:39
In this lecture, we work through example results using polynomial regression on the Gapminder data.
Step Functions5:02
In this lecture, we discuss localized step function regression.
Example: Gapminder Step Function Regression1:02
In this lecture, we look at step function regression results on the Gapminder dataset.
Regression Splines4:27
In this lecture, we introduce regression splines.
Example: Gapminder Splines2:04
In this example, we use regression splines on the Gapminder dataset.
Smoothing Splines2:06
In this lecture, we introduce smoothing splines.
Example: Gapminder Smoothing Splines0:34
This brief example uses smoothing splines on the Gapminder dataset.
Generalized Additive Models4:54
In this lecture, we outline generalized additive models.
Example: Gapminder1:53
In this lecture, we analyze the results of an example using Generalized Additive Models on the Gapminder dataset.

Outline2:56
This lecture is an outline to the classification module.
Introduction to Classification3:20
This lecture goes over the classification problem setup and discusses the similarities to regression.
Formalized Classification Setup7:35
In this lecture, we dive into the formalized classification setup.
Classification Performance Evaluation4:40
This lecture presents methods of classification performance evaluation.

KNN & Bias Variance Tradeoff10:51
This lecture introduces K-Nearest-Neighbours (KNN). We also look at the implications of the bias-variance framework in this framework.
Comparison: KNN vs. OLS15:12
This lecture investigates the differences between KNN and OLS regression for classification tasks.
Example: Gapminder 1 [Introduction to Dataset and Classification Approach]3:28
This lecture introduces the Gapminder data and outlines the approach for classification to come in the follow-up examples.
Example: Gapminder 2 [Classification in R]21:07
This worked example uses KNN and OLS to perform classification on the Gapminder dataset.
Example: Gapminder 3[ Building OLS Classifier]14:33

Intro to Logistic Regression4:57
This lecture introduces the basics of logistic regression as well as the logistic function.
Formalizing Binary Logistic Regression4:57
This lecture formalizes the foundations of logistic regression.
Example: Credit Defualt Classification12:24
This is an example on using logistic regression to model credit default.
Warning: Confounding5:13
This lecture analyzes the nuance of output interpretation in machine learning, highlighting the significance of confounding.
Multinominal Logistic Regression2:58
This lecture formulates multinomial logistic regression.
Example: Palmer Penguins15:07
This is an example of multinomial logistic regression on the Palmer Penguins dataset.

Intro to Generative Models5:19
This lecture differentiates discriminative models vs. generative models and then introduces the generative model framework.
Gaussian Bayes Derivation5:59
This lecture derives the Gaussian Bayes classifier.
Quadratic Discriminant Analysis1:28
This lecture introduces Quadratic Discriminant Analysis (QDA) as a restricted Bayes classifier.
Linear Discriminant Analysis (LDA)0:46
This lecture introduces LDA as a restricted form of QDA.
Naive Bayes Classifiers (NBC)3:23
This lecture introduces 2 variants of Naive Bayes Classifiers as forms of restricted QDA models.
Example: Palmer Penguins QDA19:07
This is an example of generative models (QDA in this video) on the Palmer Penguins dataset.
Example (cont'd): Palmer Penguins LDA and Naive Bayes6:33
This is a continuation of the Palmer Penguins example, applying other generative variants beyond QDA.

Requirements

Basic knowledge of High School mathematics

Description

Are you ready to build a strong and practical foundation of machine learning?

This comprehensive course is designed to take you from the foundational principles of machine learning to advanced techniques in regression, classification, clustering, and neural networks. Whether you're a student, a data science enthusiast, or a professional looking to sharpen your skills, this course will give you the tools and intuition you need to work effectively with real-world data.

What You'll Learn In This Course:

We begin with a conceptual overview of machine learning, exploring different types of learning paradigms—supervised, unsupervised, and more. You’ll learn how to approach problems, evaluate models, and understand common pitfalls such as overfitting, bad data, and inappropriate assumptions.

From there, we dive into Modelling:

Regression
Linear Models
Regularization (Ridge, LASSO)
Cross-Validation
Flexible Approaches like Splines and Generalized Additive Models

Classification Techniques are covered in depth, including:

Logistic Regression
KNN, Generative Models
Decision Trees
Neural Networks and Backpropagation for more Advanced Modeling.

Finally, we explore Clustering:

K-Means Clustering
Hierarchical Methods
Discussing Algorithmic Strengths, Challenges, and Evaluation Techniques.

Practice with Hands-on Examples:

We teach the concepts of Machine Learning with engaging, hands-on examples using well known datasets such as Gapminder and Palmer Penguins. Mathematical formulas are broken down and explained thoroughly step by step. Not only will you gain the theoretical understanding of Machine Learning, but also the practical intuition and experience for future projects.

With real-world datasets, detailed derivations, and clear explanations, this course bridges the gap between theory and application. By the end of the course, you will have a strong arsenal of fundamential machine learning techniques, know when and how to apply them, and understand the mathematical theories that power them—all with practical, real-world relevance.

Who this course is for:

Beginners curious in understanding Machine Learning framework
Aspiring future Machine Learning Engineers or Data Scientists
Professionals seeking to advance their careers using Machine Learning
Individuals with interest in Data Science and Mathematics

Complete Mathematical Intro to Machine Learning [2026]

What you'll learn

Explore related topics

Course content

Introduction to Machine Learning15 lectures • 1hr 28min

Introduction to Regression Models13 lectures • 1hr 33min

Regularization & Other Regression Variants6 lectures • 17min

Cross-Validation3 lectures • 16min

Non-Linear Modelling & Regression Variants10 lectures • 31min

General Regression Models and AutoML2 lectures • 11min

Introduction to Classification4 lectures • 19min

KNN and OLS for Classifiaction5 lectures • 1hr 5min

Logistic Regression6 lectures • 46min

Generative Models7 lectures • 43min

Requirements

Description

Who this course is for: