Matrix Calculus in Data Science and Machine Learning 2023-11 – Download

Descriptions

Math 0-1: Matrix Calculus in Data Science and Machine Learning. 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’ll dive into the powerful mathematics behind many of the algorithms and techniques used in these fields. By the end of this course, you will have the knowledge and skills to navigate the complex world of derivatives, gradients, and matrix optimizations. Matrix calculus is the language of machine learning and data science. In these areas, we often work with high-dimensional data, making matrices and their derivatives natural representations of our problems. Understanding matrix calculus is critical to developing and analyzing algorithms, building predictive models, and understanding the vast amounts of data at our disposal. In the first part of the course, we will learn the basics of linear and quadratic forms, as well as their derivatives. The linear form is found 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 delve into quadratic forms, which are fundamental to understanding optimization problems encountered in regression, portfolio optimization in finance, signal processing, and control theory.

What will you learn

Derivation of matrix and vector derivatives for linear and quadratic forms.
Solve general optimization problems (least squares, Gaussian, financial portfolio).
Understand and implement gradient descent and Newton’s method.
Learn to use the Matrix cookbook.