Hands-On Learning Theory

Semester: 2026 Semester 1, also offered on 2025 Semester 2, 2025 Semester 1, 2024 Semester 2 and 2024 Semester 1
Time and place: The University of Melbourne, Friday 12-1pm, Melbourne Connect 2206
Organizer: Jean Honorio

Imagine you run your favorite machine learning algorithm and obtain impressive results. Some weeks later, you collect more data and your algorithm does not perform very well. What happened? Is your algorithm wrong? Do you need to collect more data for learning? Should you use another algorithm?

In these meetings, we will analyze when an algorithm works or not, with respect to several aspects, such as how much training data is needed, how much computation, etc. We will learn the main tools for proving theorems and proposing new algorithms, proving their convergence, necessary/sufficient number of samples, etc.

Technically speaking, these meetings will mainly focus on non-asymptotic analysis of the convergence and statistical efficiency of algorithms. We will introduce several concepts and proof techniques from statistical learning theory, information theory and optimization. The meetings will include topics such as concentration bounds, empirical risk minimization, PAC-Bayes, Rademacher/Gaussian complexity, Karush-Kuhn-Tucker conditions, primal-dual witness, convergence rates, restricted strong convexity, Fano's inequality, etc.

Basic knowledge from calculus and linear algebra is required. Some knowledge or experience with machine learning or data mining is welcome. Necessary concepts from statistics and optimization will be provided during the meetings.

Schedule

Date Topic (Tentative) Notes
Fri, Mar 13 Lecture 1: Markov's inequality, Chebyshev's inequality
Fri, Mar 20 Lecture 2: Hoeffding's inequality, empirical risk minimization with a finite hypothesis class 12.30-1.30pm at Melbourne Connect 3209
Fri, Mar 27 Lecture 8: restricted strong convexity, compressed sensing
Fri, Apr 3 Holiday
Fri, Apr 10     (lecture continues)
Fri, Apr 17 Lecture 9: primal-dual witness method, support recovery
Fri, Apr 24     (lecture continues) 12.30-1.30pm at Melbourne Connect 3209
Fri, May 22 Lecture 7: deterministic optimization, convergence rates