Spring 2023 - CMPT 727 G100

Mathematical and Probabilistic Foundations of Machine Learning (3)

Class Number: 6488

Delivery Method: In Person


  • Course Times + Location:

    Jan 4 – Apr 11, 2023: Wed, 1:30–2:20 p.m.

    Jan 4 – Apr 11, 2023: Fri, 12:30–2:20 p.m.



Using machine learning algorithms effectively requires understanding their theoretical and conceptual basis. Covers mathematical and probabilistic foundations of machine learning, placing learning methods in a unified framework based on Bayesian reasoning. Students will acquire skills for formulating models, deriving optimization algorithms, and choosing effective approaches for a given learning problem. Topics include parameter estimation, optimization, linear classification and regression, regularization, and probabilistic graphical models.


Why we're offering this course: Machine learning now plays a central role in hundreds of fields. All learning methods have common underpinnings based on probability and statistics, but these are not widely understood. This course aims to give students a probabilistic foundation for machine learning and an understanding of probabilistic machine learning methods.

After you complete this course, you will be able to:
* Design and implement probabilistic machine learning techniques including: probabilistic graphical models, discrete and continuous distributions, maximum likelihood estimation, EM algorithm inference, sampling-based inference methods, MCMC, variational inference.
* Understand concepts such as: prior, posterior, likelihood, overfitting, bias-variance tradeoff, likelihood, regularization.
* Choose between probabilistic machine learning methods, understand what aspects of a data set influence machine learning performance. and foresee which will perform best

Who should take this course? This course is intended for graduate students with an interest in machine learning or big data. You should take this course if:
* You intend to use or develop machine learning in your research or work.
* You are interested in fields where probabilisitic machine learning is important including: vision, natural language processing/understanding, medical imaging, robotics, smart cities.
* You want to understand statistical behavior of machine learning methods at a deep level.

Prerequisites: No official prerequisites. However, the course assumes basic knowledge of machine learning (e.g. CMPT 726), probability (e.g. STAT 270) and linear algebra (e.g. MATH 240). The course is open to advanced undergraduates with permission.


  • Probabilistic graphical models
  • Discrete and continuous distributions
  • Maximum likelihood estimation
  • EM algorithm
  • Bayesian probability



Grading will be based on written and coding assignments and participation in group problem solving sessions.



“Probabilistic machine learning”, Patrick Murphy. https://probml.github.io/pml-book/


Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:


SFU’s Academic Integrity website http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating. Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html