Registration Deadline: January 21st, 2025

Instructor: Professor Maia Fraser, University of Ottawa

Course Dates: January 8th - April 4th, 2025
Mid-Semester Break: February 17th - 21st, 2025
Lecture Times: Wednesdays, 4:00 PM - 5:20 PM (ET) | Fridays, 2:30 PM - 3:50 PM (ET)
Office Hours: Fridays, 10:30 AM - 12:30 PM (via Zoom)

Registration Fee: PSU Students - Free | Other Students - CAD$500

Capacity Limit: 50 students

Format: Hybrid synchronous delivery

• In-Person (for uOttawa students)
• Online via Zoom (for non-uOttawa students)

Course Description

This course will introduce mathematics graduate students to Machine Learning, giving an overview of methods and their properties from a mathematical point of view. The course assignments and project will involve adjustable amounts of theoretical and practical work. No previous experience in machine learning or coding is required, just graduate-level mathematical maturity, curiosity about machine learning, and the willingness to acquire some coding experience as we go, though the amount of this can be adjusted.

We will start with a brief look at the formalization of learning. We will then see this formulation in action through a variety of linear techniques: first, we revisit the familiar Ordinary Least Squares algorithm and some of its variants from this perspective, then Discriminant Analysis; finally, we cover Support Vector Machines (SVMs) and their underlying mathematics. We then look at reproducing kernel Hilbert spaces (RKHS) and the so-called kernel trick which gives rise to a wide-range of non-linear learning algorithms known as kernel methods; these are “kernelized” versions of linear methods. The core of the course then focuses on learning theory: VC Theory and PAC learning. We then consider more elaborate learning methods, such as boosting, from this perspective, and we also study neural networks (Perceptron, CNNs) from a mathematical point of view. Finally, depending on time and student interest, we will cover additional topics chosen from: Reinforcement Learning, Manifold Learning, Algorithmic Stability...

Text: Foundations of Machine Learning by Mohri et al (2012/2018) https://cs.nyu.edu/~mohri/mlbook/, plus handouts of mine and links to various online resources.

Course work: There will be 3 homework assignments, one midterm (in-person for uOttawa students, online for others), and a final project that is done in small teams over the space of 4 weeks. On homeworks and project there will be some flexibility in the amount of theory vs. implementation that you do, as well as the types of data you choose to work with. The hope is to tailor this course to your particular interests and background. No instruction in coding will be given but there is ample time to learn as you go and the demands will grow gradually and remain moderate. The midterm will include some basic questions to test familiarity with the material, as well as one or two proof-based questions. Submission of homework and project will be via the Fields Moodle (as well as submission of the midterm for non-uOttawa students).

Grading scheme: Tentative only - may be adjusted depending on enrolment and TA support. HW1 and HW2 will be graded and each count for 14% of your grade, HW3 will be pass-fail and count for 2% of your grade, the midterm will count for 30% and the final project (done in small groups) for 40% - it will serve as a take-home exam.