Calculus for Machine Learning, Level III: Partial Derivatives (ML Foundations Series)

• Intro to Partial Derivatives: This class expands from single-variable to multi-variable calculus, focusing on partial derivatives.
• The Key to Gradients: By emphasizing the role of partial derivatives in creating gradients, the course directly addresses gradient descent, the mechanism through which most ML models adjust and improve based on data.
• Foundation for Gradient-Based Optimization: As an essential prerequisite for the most advanced topics in the ML Foundations series, this course prepares students for understanding the gradient-based learning detailed in the Calculus for Machine Learning, Level IV and Optimization classes.

The Machine Learning Foundations series of online trainings provides a comprehensive overview of all the subjects — mathematics, statistics, and computer science — that underlie contemporary machine learning techniques, including deep learning and other artificial intelligence approaches. Extensive curriculum detail can be found at the course’s GitHub repo.

All of the classes in the ML Foundations series bring theory to life through the combination of vivid full-color illustrations, straightforward Python examples within hands-on Jupyter notebook demos, and comprehension exercises with fully worked solutions. The focus is on providing you with a practical, functional understanding of the content covered. Context will be given for each topic, highlighting its relevance to machine learning. You will be better positioned to understand cutting-edge machine learning papers and you will be provided with resources for digging even deeper into topics that pique your curiosity.

There are 14 classes in the series, organized into four subject areas:

1. Linear Algebra (three classes)  

• Linear Algebra for Machine Learning: Intro
• Linear Algebra for Machine Learning, Level II: Matrix Tensors
• Linear Algebra for Machine Learning, Level III: Eigenvectors

2. Calculus (four classes)   

• Calculus for Machine Learning: Intro
• Calculus for Machine Learning, Level II: Automatic Differentiation
• Calculus for Machine Learning, Level III: Partial Derivatives
• Calculus for Machine Learning, Level IV: Gradients & Integrals

3. Probability and Statistics (four classes)  

• Intro to Probability
• Probability II and Information Theory
• Intro to Statistics
• Statistics II: Regression and Bayesian

4. Computer Science (three classes)   

• Intro to Data Structures and Algorithms
• DSA II: Hashing, Trees, and Graphs
• Optimization

Each of the four subject areas are fairly independent; however, theory within a given subject area generally builds over the 3-4 classes — topics in later classes of a given subject area often assume an understanding of topics from earlier classes. Work through the individual classes based on your particular interests or your existing familiarity with the material.

(Note that at any given time, only a subset of the ML Foundations classes will be scheduled and open for registration.)

This class, Calculus for Machine Learning, Level III: Partial Derivatives, builds on the single-variable derivative calculus of Calculus I-II to introduce partial derivatives. Understanding partial derivatives is essential because they are collected to form gradients of learning. It is by adjusting model parameters based on these gradients that most machine learning algorithms are able to learn from data (i.e., via gradient descent). The content covered in this class is itself foundational for several other classes in the Machine Learning Foundations series, especially Calculus for Machine Learning, Level IV and the final class in the series, on Optimization.