Multivariable calculus: Machine Learning Companion

Machine learning companion #

Multivariable calculus and linear algebra are the language of modern machine learning. These labs, demos, and exercises take ideas from the course, such as feature vectors, the dot product, gradients, and the chain rule, and show where they appear in machine learning.

Automated language identification: A common machine learning task is to identify the language of a written text sample. This lab introduces and evaluates the method of cosine similarity as a solution to this task. Image: Conor O’Sullivan.

arrows fanning out from the origin over a cloud of points

Cosine similarity and large language models: Cosine similarity, introduced in the language lab, also appears in large language model embedding layers.

Data sets and feature vectors: An introduction to a few standard machine learning data sets and ways to format the data using feature vectors.

Clustering and classification: A brief overview of one of the fundamental problems in machine learning. How should similarity be measured to produce clusters or groups among feature vectors?

Regression: A collection of labs and exercises introducing data models, regression, and methods of evaluating the quality of predictions made by them.

Neural networks: A collection of labs and activities introducing neural networks in the context of multivariable calculus.