Math 0-1: Matrix Calculus in Data Science & Machine Learning

About this course

Welcome to the exciting world of Matrix Calculus, a fundamental tool for understanding and solving problems in machine learning and data science. In this course, we will dive into the powerful mathematics that underpin many of the algorithms and techniques used in these fields. By the end of this course, you'll have the knowledge and skills to navigate the complex landscape of derivatives, gradients, and optimizations involving matrices.

Course Objectives:

• Understand the basics of matrix calculus, linear and quadratic forms, and their derivatives.
• Learn how to utilize the famous Matrix Cookbook for a wide range of matrix calculus operations.
• Gain proficiency in optimization techniques like gradient descent and Newton's method in one and multiple dimensions.
• Apply the concepts learned to real-world problems in machine learning and data science, with hands-on exercises and Python code examples.

Why Matrix Calculus? Matrix calculus is the language of machine learning and data science. In these fields, we often work with high-dimensional data, making matrices and their derivatives a natural representation for our problems. Understanding matrix calculus is crucial for developing and analyzing algorithms, building predictive models, and making sense of the vast amounts of data at our disposal.

Section 1: Linear and Quadratic Forms In the first part of the course, we'll explore the basics of linear and quadratic forms, and their derivatives. The linear form appears in all of the most fundamental and popular machine learning models, including linear regression, logistic regression, support vector machine (SVM), and deep neural networks. We will also dive into quadratic forms, which are fundamental to understanding optimization problems, which appear in regression, portfolio optimization in finance, signal processing, and control theory.

The Mat

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