Machine Learning Foundations

A foundational course covering the essential mathematical prerequisites—Calculus, Linear Algebra, Optimization, and Probability—necessary for a comprehensive understanding of Machine Learning.

This course built the solid mathematical and statistical bedrock upon which modern machine learning is built. It was designed to provide a comprehensive understanding of the core concepts that underpin ML algorithms. We delved deep into the essential pillars: linear algebra for data representation and dimensionality reduction (Eigenvectors, SVD, PCA); calculus and optimization theory for training models (unconstrained and constrained optimization, Lagrange multipliers); and probability for modeling uncertainty (probabilistic models, exponential family, and the Expectation-Maximization algorithm). This course provided the “why” behind the “how” of machine learning.

Instructors

Course Schedule & Topics

The course is structured over 12 weeks, focusing on the mathematical and statistical fundamentals of machine learning.

Week Primary Focus Key Topics Covered
1 Introduction to Machine Learning An overview of the field and the role of foundational mathematics.
2 Review of Calculus Essential calculus concepts required for optimization in machine learning.
3 Linear Algebra: Least Squares Using linear algebra to solve Least Squares Regression problems.
4 Linear Algebra: Eigen-decomposition Understanding eigenvalues and eigenvectors.
5 Linear Algebra: Symmetric Matrices Special properties and applications of symmetric matrices.
6 Linear Algebra: SVD & PCA Singular Value Decomposition (SVD) and its application in Principal Component Analysis (PCA).
7 Unconstrained Optimization Techniques for solving optimization problems without constraints.
8 Convex Optimization Fundamentals of convex sets, functions, and optimization problems.
9 Constrained Optimization Lagrange Multipliers and framing Logistic Regression as an optimization problem.
10 Probabilistic Models in ML Examples of probabilistic models and their use in machine learning.
11 Exponential Family of Distributions Understanding the exponential family and its importance in generalized linear models.
12 Parameter Estimation & EM Methods for parameter estimation, including the Expectation-Maximization (EM) algorithm.

Material used