Mathematical Introduction To Machine Learning

A mathematical journey through common machine learning frameworks in regression, classification, and clustering.

What you'll learn

Learn basics of machine learning, including both supervised learning and unsupervised learning.

Grasp the mathematical foundations of the most common machine learning framework.

Be able to differentiate appropriate machine learning models for specific use cases (e.g. regression vs. classification vs. clustering).

Have a well-tailored toolbox of machine learning algorithms to apply to data science problems.

Be familiar with how to fit machine learning models in R and Python.

Be familiar with the challenges ones can face in machine learning.

Requirements

Linear Algebra

Probability

Statistics

Multivariate Differential Calculus

Beginner experience in R

Beginner experience in Python

Description

Are you ready to gain a deep and practical understanding 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.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 regression, covering linear models, regularization (Ridge, LASSO), cross-validation, and flexible approaches like splines and Generalized Additive Models—all illustrated with hands-on examples using datasets like Gapminder and Palmer Penguins.Classification techniques are covered in depth, including logistic regression, KNN, generative models, and decision trees, along with neural networks and backpropagation for more advanced modeling.Finally, we explore clustering, from k-means to hierarchical methods, discussing algorithmic strengths, challenges, and evaluation techniques.With real-world datasets, detailed derivations, and clear explanations, this course bridges the gap between theory and application.

Overview

Section 1: Introduction to Machine Learning

Lecture 1 Outline

Lecture 2 Overview of Machine Learning

Lecture 3 Supervised Learning Introduction

Lecture 4 Why Test Data?

Lecture 5 Unsupervised Machine Learning

Lecture 6 Other Types of Learning

Lecture 7 Supervised Learning Example: Mushroom Dataset

Lecture 8 Machine Learning Issues: Bad Data

Lecture 9 Machine Learning Issues: Under-Over fitting

Lecture 10 Intro to Machine Learning Formalism

Lecture 11 Model Evaluation

Lecture 12 Machine Learning Trade-Offs

Lecture 13 Estimating the Regression Function

Lecture 14 More Complex Regression Functions

Lecture 15 The Bias-Variance Trade-Off

Section 2: Introduction to Regression Models

Lecture 16 Outline

Lecture 17 Intro and Motivating Example

Lecture 18 Intro to Simple Linear Regression

Lecture 19 With Intercept Model

Lecture 20 Example: Gentoo Penguins

Lecture 21 Derivation: Multiple Linear Regression

Lecture 22 Example: Gapminder

Lecture 23 Interpretation of OLS Output

Lecture 24 Hypothesis Testing

Lecture 25 Confidence Intervals

Lecture 26 Model Evaluation

Lecture 27 Feature Selection

Lecture 28 Other Questions

Section 3: Regularization & Other Regression Variants

Lecture 29 Intro to Regularization

Lecture 30 Ridge Regression

Lecture 31 Best Subset Selection

Lecture 32 LASSO Regularization

Lecture 33 Other Regression Variants

Lecture 34 Example: Gapminder Regularized Regression

Section 4: Cross-Validation

Lecture 35 K-Fold Cross Validation

Lecture 36 Cross Validation on Gapminder

Lecture 37 Hyperparameter Selection for Regularization

Section 5: Non-Linear Modelling & Regression Variants

Lecture 38 Non-Linear Modelling and Basis Functions

Lecture 39 Example: Polynomial Gapminder

Lecture 40 Step Functions

Lecture 41 Example: Gapminder Step Function Regression

Lecture 42 Regression Splines

Lecture 43 Example: Gapminder Splines

Lecture 44 Smoothing Splines

Lecture 45 Example: Gapminder Smoothing Splines

Lecture 46 Generalized Additive Models

Lecture 47 Example: Gapminder

Section 6: General Regression Models and AutoML

Lecture 48 General Model Selection

Lecture 49 Example: Gapminder AutoML

Section 7: Introduction to Classification

Lecture 50 Outline

Lecture 51 Introduction to Classification

Lecture 52 Formalized Classification Setup

Lecture 53 Classification Performance Evaluation

Section 8: KNN and OLS for Classifiaction

Lecture 54 KNN & Bias Variance Tradeoff

Lecture 55 Comparison: KNN vs. OLS

Lecture 56 Example: Gapminder 1 [Introduction to Dataset and Classification Approach]

Lecture 57 Example: Gapminder 2 [Classification in R]

Lecture 58 Example: Gapminder 3[ Building OLS Classifier]

Section 9: Logistic Regression

Lecture 59 Intro to Logistic Regression

Lecture 60 Formalizing Binary Logistic Regression

Lecture 61 Example: Credit Defualt Classification

Lecture 62 Warning: Confounding

Lecture 63 Multinominal Logistic Regression

Lecture 64 Example: Palmer Penguins

Section 10: Generative Models

Lecture 65 Intro to Generative Models

Lecture 66 Gaussian Bayes Derivation

Lecture 67 Quadratic Discriminant Analysis

Lecture 68 Linear Discriminant Analysis (LDA)

Lecture 69 Naive Bayes Classifiers (NBC)

Lecture 70 Example: Palmer Penguins QDA

Lecture 71 Example (cont'd): Palmer Penguins LDA and Naive Bayes

Section 11: Tree-Based Learning

Lecture 72 Introduction to Tree Based Methods

Lecture 73 Example: Gapminder 1 [Building the Model]

Lecture 74 Example: Gapminder 2 [ Analyzing the Model]

Lecture 75 Building a Regression Tree

Lecture 76 Tree Pruning

Lecture 77 Classification Trees

Lecture 78 Example: Iowa Housing Data

Section 12: Neural Networks

Lecture 79 Intro to Neural Networks & Activation Functions

Lecture 80 Derivation: Fully Connected Feed Forward Neural Networks pt1

Lecture 81 Derivation: Fully Connected Feed Forward Neural Networks pt2

Lecture 82 Derivation: Fully Connected Feed Forward Neural Networks pt3

Lecture 83 Example: Computer Vision w/ Neural Networks

Section 13: Introduction to Clustering

Lecture 84 Outline

Lecture 85 Clustering Algorithms and Theory

Lecture 86 Generalities

Lecture 87 Clustering Framework & Applications

Lecture 88 What is a Cluster?

Lecture 89 Clustering Approaches

Lecture 90 Distance, Similarity, and Dissimilarity

Lecture 91 Data Transformations for Clustering

Lecture 92 Challenges in Clustering

Section 14: K-Means Clustering

Lecture 93 k-Means Clustering

Lecture 94 k-Means Algorithm

Lecture 95 Strengths and Limitations of k-Means

Lecture 96 Example: Penguins Dataset

Lecture 97 Example: Gapminder Dataset

Section 15: Hierarchical Clustering

Lecture 98 Introduction to Hierarchical Clustering

Lecture 99 Introduction to AGNES and DIANA

Lecture 100 A Formal Look into AGNES and DIANA

Lecture 101 Linkage Strategies

Lecture 102 Example: Penguins Dataset

Lecture 103 Example: Gapminder Dataset

Section 16: Clustering Evaluation

Lecture 104 Intro to Clustering Evaluation

Lecture 105 Clustering Assessment

Lecture 106 Clustering Quality Measures

Lecture 107 Internal Validation

Lecture 108 Cluster Quality Metrics

Lecture 109 Relative Validation

Lecture 110 External Validation and Model Selection

Future machine learning engineers or data scientists looking to deeply understand machine learning.,Mathematically curious individuals.