Foundations of Statistical Learning & Algorithms

Overview

This course covers linear algebra, probability, and optimization. It begins with systems of equations, matrix operations, vector spaces, and eigenvalues. Advanced topics include Cholesky and singular value decomposition. Probability modules address Bayes' theorem, Gaussian distribution, and inference techniques. The course concludes with model selection methods and an introduction to optimization.

Syllabus

Introduction to Linear Algebra and Vector Spaces

This module provides a foundational understanding of linear algebra concepts essential for statistical learning and algorithms. You will explore the principles of linear systems, matrix operations, vector spaces, orthogonality, and projections. These topics will lay the groundwork for understanding more advanced machine learning and statistical modeling techniques.

Linear Transformation and Matrix Decomposition

This module covers essential linear algebra concepts, focusing on linear mappings, eigenvectors, eigenvalues, Cholesky decomposition, and singular value decomposition. You'll learn to apply linear mappings, interpret eigenvectors and eigenvalues, and explore the Cholesky decomposition for symmetric, positive definite matrices. Additionally, you'll delve into singular value decomposition and its applications. The lessons include linear independence, linear mappings, eigenvalues and eigenvectors, Cholesky decomposition, and singular value decomposition, providing a comprehensive understanding of these critical topics.

Probability Foundations for Statistical Learning

This module focuses on essential probability concepts and their applications in machine learning. You will explore the sum rule, product rule, and Bayes' theorem, understanding how these principles are applied to solve complex problems. Additionally, you'll learn to apply Bayesian inference to estimate hidden variables from observed data, enhancing your ability to make informed predictions and decisions in machine learning contexts. These topics will provide a solid foundation for understanding and implementing probabilistic models in various machine learning scenarios.

Introduction to Model Evaluation and Optimization

This module covers key techniques for enhancing machine learning models. You will learn to minimize the error or loss of a model through various optimization methods. Additionally, you'll explore different cross-validation techniques to assess model performance and generalizability. By examining various optimization techniques, you'll improve model accuracy and efficiency. These topics will equip you with the skills to fine-tune and validate your machine learning models effectively.