Free online courseMatrix Calculus For Machine Learning

Course Description

Matrix Calculus For Machine Learning is a detailed and technical course tailored for individuals in the Information Technology sector, specifically within the realm of Artificial Intelligence. This engaging course is structured to expand your expertise in matrix calculus, a critical area of knowledge crucial for advanced machine learning applications. Over the span of 13 hours and 55 minutes, you will delve deep into the fascinating world of matrix operations and their derivatives.

The course starts with an introductory lecture that sets the stage by illuminating the significance and motivation behind learning matrix calculus in the context of machine learning. As you progress, you will be introduced to the foundational concept of derivatives viewed as linear operators. This pivotally connects traditional calculus to the sophisticated algebraic operations on matrices, providing a fresh perspective that is both illuminating and practical for machine learning tasks.

Moving on to higher dimensions, the course meticulously covers the concept of Jacobians and matrix functions, exploring how derivatives operate in multi-dimensional spaces. You'll also encounter the powerful technique of vectorization, which is essential for efficient computation in machine learning algorithms.

The subsequent lectures introduce you to Kronecker products and their relationship with Jacobians, followed by a dive into finite-difference approximations—an alternative numerical method for estimating derivatives. These concepts are pivotal for understanding the intricacies of numerical analysis in the context of matrix calculus.

As you approach Lecture 4, the course takes an intriguing turn towards gradients and inner products in various vector spaces. This lecture is further enriched by discussions on nonlinear root finding, optimization techniques, and adjoint gradient methods, which are instrumental in developing and fine-tuning machine learning models.

Lecture 5 brings a detailed analysis of the derivative of matrix determinants and inverses, supplemented by the concepts of forward automatic differentiation via dual numbers and differentiation on computational graphs. These techniques are key tools for automatic differentiation, which is widely used in training neural networks.

In Lecture 6, the course dives into the adjoint differentiation of ODE solutions and the calculus of variations, coupled with insights into the gradients of functionals. These advanced topics are critical for understanding the dynamic systems and functional optimization problems often encountered in machine learning.

Lecture 7 delves into the differentiation of random functions, second derivatives, bilinear forms, and Hessian matrices. These are vital components for comprehending optimization landscapes and fine-tuning machine learning algorithms.

The final lecture of the course introduces the derivatives of eigenproblems and revisits automatic differentiation on computational graphs, cementing your understanding and equipping you with the knowledge to tackle complex machine learning challenges.

This course is a treasure trove of knowledge for anyone looking to deepen their understanding of matrix calculus in the context of machine learning, offering a robust foundation essential for advanced studies and innovative developments in the field of Artificial Intelligence.