CPSC 532S: Modern Statistical Learning Theory – 2021-22 W2

Schedule

SSBD below refers to the book of Shalev-Shwartz and Ben-David; MRT to that of Mohri, Rostamizadeh, and Talwakar. Italicized entries are tentative.

Logistics

The course meets in person in DMP 101 (since Feb 14th) and is also available on Zoom: the meeting link and recordings are available on Canvas and Piazza.

Grading scheme: 70% assignments (including a small project), 30% final.

The lowest assignment grade (not including the project) will be dropped. The project counts as one assignment. Assignments should be done in LaTeX – not handwritten or in a word processor. Hand-in on Gradescope, as described on Piazza.

There will be one “big assignment” which serves as a (small) project: something on the scale of doing some experiments to explore a paper, doing a lit review in a particular area, extending / unifying a few papers, etc. A proposal will be due beforehand; details to come.

The final exam may be take-home, synchronous online, or in-person; TBD.

There may also be some paper presentations later in the course, in which case the paper presenters will be able to use that to replace part of an assignment grade. This is dependent on the COVID situation and other factors; TBD.

Overview

The brief idea of the course: when should we expect machine learning algorithms to work? What kinds of assumptions do we need to be able to be able to rigorously prove that they will work?

Definitely covered: PAC learning, VC dimension, Rademacher complexity, concentration inequalities. Probably: PAC-Bayes, analysis of kernel methods, margin bounds, stability. Maybe: limitations of uniform convergence, analyzing deep nets via neural tangent kernels, provable gaps between kernel methods and deep learning, online learning, feasibility of private learning, compression-based bounds.

There will be some overlap with CPSC 531H: Machine Learning Theory (Nick Harvey's course, last taught in 2018), but if you've taken that course, you'll still get something out of this one. We'll cover less on optimization / online learning / bandits than that course did, and try to cover some more recent ideas used in contemporary deep learning theory.

(This course is unrelated to CPSC 532S: Multimodal Learning with Vision, Language, and Sound, from Leon Sigal.)

Prerequisites

There are no formal prerequisites. I will roughly assume:

• Basic "mathematical maturity": familiarity with reading and writing proofs, recognizing a valid proof, etc. If you've taken a third-year math course or similar, you should be fine.
• Comfort with linear algebra, multivariable calculus, basic probability theory, and basic analysis of algorithms.
• Ideally, a basic understanding of machine learning, as in CPSC 340. If you don't have this, you should still be able to get by, but might have to do a little more reading on your own; I'll provide some resources.
• Ideally, familiarity with programming in a machine learning / statistical context, e.g. being comfortable with numpy and PyTorch/TensorFlow/etc. This course will not require programming, but there will be some assignment and project options that may be easier / more fruitful / more fun if you're comfortable with it.

Resources

Learning theory textbooks and surveys:

• Understanding Machine Learning: From Theory to Algorithms (Shai Shalev-Shwartz, Shai Ben-David; 2014) – a very readable (free) book that covers a significant portion of our material
• Foundations of Machine Learning (Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwakar; second edition 2018) – free textbook, also quite good
• Introduction to Statistical Learning Theory (Olivier Bousquet, Stéphane Boucheron, Gábor Lugosi; 2003) – 40-page survey of classics
• On the Mathematical Foundations of Learning (Felipe Cucker, Steve Smale; 2001) – 50-page survey of classics
• Deep learning theory lecture notes (Matus Telgarsky; ongoing updates) – overview including some quite modern stuff; we'll pull from here especially later in the course
• An Introduction to Computational Learning Theory (Michael Kearns, Umesh Vazirani; 1994; that link should get you a copy with a UBC login) – a book from a much more CS theory point of view. A nice complement to what we'll cover in this course.

If you need to refresh your linear algebra or other areas of math:

• Mathematics for Machine Learning (Marc Deisenroth, Aldo Faisal, Cheng Soon Ong; 2020) – a nice overview. Unfortunately their probability chapter doesn't use a measure theoretic point of view (see below), but if you don't know the material in it, you probably should.

Resources on learning measure-theoretic probability (not required to know this stuff in detail, but you might find it helpful):

• A Measure Theory Tutorial (Measure Theory for Dummies) (Maya Gupta) – 5 pages, just the basics
• Measure Theory, 2010 (Greg Hjorth) – 110 pages but comes recommended as both thorough and readable
• A Probability Path (Sidney Resnick) – frequently recommended textbook aimed at non-mathematicians to learn it in detail, but it's a full-semester textbook scale of detail; available if you log in via UBC
• There are also lots of other places, of course; e.g. the probability textbooks by Billingsley, Klenke, and Williams are (I think) classics.

Similar courses:

• UBC CPSC 531H: Machine Learning Theory (Nick Harvey)
• MIT 9.520: Statistical Learning Theory and Applications (Tomaso Poggio, Loreno Rosasco, Alexander Rakhlin, Ardrzej Banburski)
• TTIC 31120: Computational and Statistical Learning Theory (Nati Srebro)
• CMU 10-806: Foundations of Machine Learning and Data Science (Nina Balcan, Avrim Blum)
• UIUC ECE 598MR: Statistical Learning Theory (Maxim Raginsky)