Mathematics for AI

Hi there!

Welcome to the Machine Learning 1 (ML1) course here at MSc Artificial Intelligence from the University of Amsterdam. These notes are provided to help you familiarize yourself with the ‘prior knowledge’ needed to follow the ML1 course. In practice, however, you will probably not know all the material here, and please do not feel discouraged by that. We advise you to read through these notes and see which things you already knew and which things you need to brush up on.

The document is divided into three parts: linear algebra, multivariate calculus, and a general introduction to machine learning. The first section aims to refresh your knowledge about vectors, matrices, linear transformations, determinants, bases, orthonormal projections, eigen decompositions, and similar topics. The second section is focused on calculus in higher dimensions, essentially generalizing the derivative from standard (real) functions to real functions between higher-dimensional Euclidean spaces. The last section will zoom into the machine learning problem, the actual reason you are probably reading these notes, to begin with. It is a concise sketch of the general problem you will be facing for the next weeks.

If you see any errors in this document, please write us and we will make sure to address them as soon as possible. Moreover, feel free to share this document with whoever might profit from it. Good luck with your studies!

Floor & Tin & Gabriele

Note

This project is under active development.

Contents

• Linear Algebra
  • Vector spaces
  • Basis
  • Dot product
  • Linear Operators
  • Change of Basis
• Calculus
  • What are derivatives and why should we care?
  • Univariate derivatives
  • Multivariate derivatives
  • Jacobians
• Statistical Learning
• Derivative Rules
  • Standard derivatives
  • Derivative of combined functions